Identifying Equivalent Algebraic Expressions — Practice
Identifying Equivalent Algebraic Expressions — Practice. Practice questions to deepen understanding of identifying equivalent algebraic expressions. Online math practice with full solutions and step-by-step explanations.
Practice identifying equivalent expressions — distributive law, factoring, and special product formulas.
Question 1
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(8(x + 11)\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(8(x + 11)\)
⟺
\(8x + 88\)
Expand the parentheses
\(8 \cdot x + 8 \cdot 11 = 8x + 88\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(8x + 88\) ✓
Question 2
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(8x - 4x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(8x - 4x\)
⟺
\(4x\)
Subtract like terms
\((8-4)x = 4x\)
💡 Think of x as a computer:
\(8x - 4x = 4x\)
8 computers
💻💻💻💻💻💻💻💻
minus
4 computers
💻💻💻💻
=
4 computers
💻💻💻💻
✨ 8 computers minus 4 computers = 4 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(4x\) ✓
Question 3
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(5x + 5x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(5x + 5x\)
⟺
\(10x\)
Add like terms
\((5+5)x = 10x\)
💡 Think of x as a computer:
\(5x + 5x = 10x\)
5 computers
💻💻💻💻💻
plus
5 computers
💻💻💻💻💻
=
10 computers
💻💻💻💻💻💻💻💻💻💻
✨ 5 computers plus 5 computers = 10 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(10x\) ✓
Question 4
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(5(x + 3)\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(5(x + 3)\)
⟺
\(5x + 15\)
Expand the parentheses
\(5 \cdot x + 5 \cdot 3 = 5x + 15\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(5x + 15\) ✓
Question 5
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(8x - 3x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(8x - 3x\)
⟺
\(5x\)
Subtract like terms
\((8-3)x = 5x\)
💡 Think of x as a computer:
\(8x - 3x = 5x\)
8 computers
💻💻💻💻💻💻💻💻
minus
3 computers
💻💻💻
=
5 computers
💻💻💻💻💻
✨ 8 computers minus 3 computers = 5 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(5x\) ✓
Question 6
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(5x + 4x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(5x + 4x\)
⟺
\(9x\)
Add like terms
\((5+4)x = 9x\)
💡 Think of x as a computer:
\(5x + 4x = 9x\)
5 computers
💻💻💻💻💻
plus
4 computers
💻💻💻💻
=
9 computers
💻💻💻💻💻💻💻💻💻
✨ 5 computers plus 4 computers = 9 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(9x\) ✓
Question 7
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(9(x + 7)\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(9(x + 7)\)
⟺
\(9x + 63\)
Expand the parentheses
\(9 \cdot x + 9 \cdot 7 = 9x + 63\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(9x + 63\) ✓
Question 8
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(9x - 2x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(9x - 2x\)
⟺
\(7x\)
Subtract like terms
\((9-2)x = 7x\)
💡 Think of x as a computer:
\(9x - 2x = 7x\)
9 computers
💻💻💻💻💻💻💻💻...
minus
2 computers
💻💻
=
7 computers
💻💻💻💻💻💻💻
✨ 9 computers minus 2 computers = 7 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(7x\) ✓
Question 9
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(4x + 5x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(4x + 5x\)
⟺
\(9x\)
Add like terms
\((4+5)x = 9x\)
💡 Think of x as a computer:
\(4x + 5x = 9x\)
4 computers
💻💻💻💻
plus
5 computers
💻💻💻💻💻
=
9 computers
💻💻💻💻💻💻💻💻💻
✨ 4 computers plus 5 computers = 9 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(9x\) ✓
Question 10
2.50 pts
🔄 Identifying Equivalent Expressions ⭐
Which expression is equivalent to the following?
\(8(x + 7)\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(8(x + 7)\)
⟺
\(8x + 56\)
Expand the parentheses
\(8 \cdot x + 8 \cdot 7 = 8x + 56\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(8x + 56\) ✓
Question 11
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(x \cdot 3 + 13\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(x \cdot 3 + 13\)
⟺
\(3x + 13\)
Commutative law of multiplication
\(x \cdot a = a \cdot x = ax\)
💡 Think of x as a computer:
\(x \cdot 3 + 13 = 3x + 13\)
1 computers
💻
=
1 computers
💻
✨ 1 computers = 1 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(3x + 13\) ✓
Question 12
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(2x + 10\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(2x + 10\)
⟺
\(10 + 2x\)
Commutative law of addition
\(a + b = b + a\)
Therefore
\(2x + 10 = 10 + 2x\)
💡 Think of x as a computer:
\(2x + 10 = 10 + 2x\)
2 computers
💻💻
=
2 computers
💻💻
✨ 2 computers = 2 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(10 + 2x\) ✓
Question 13
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(8x + 2y + 6\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(8x + 2y + 6\)
⟺
\(6 + 8x + 2y\)
Order of addition doesn't matter
\(8x + 2y + 6 = 6 + 8x + 2y\)
💡 Think of x as a computer:
(With different variables, group each kind separately)
Variable x:
💻💻💻💻💻💻(8)=💻💻💻💻💻💻(8x)
Variable y:
📱📱=📱📱(2y)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(6 + 8x + 2y\) ✓
Question 14
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(x \cdot 11 + 12\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(x \cdot 11 + 12\)
⟺
\(11x + 12\)
Commutative law of multiplication
\(x \cdot a = a \cdot x = ax\)
💡 Think of x as a computer:
\(x \cdot 11 + 12 = 11x + 12\)
1 computers
💻
=
1 computers
💻
✨ 1 computers = 1 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(11x + 12\) ✓
Question 15
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(7x + 14\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(7x + 14\)
⟺
\(14 + 7x\)
Commutative law of addition
\(a + b = b + a\)
Therefore
\(7x + 14 = 14 + 7x\)
💡 Think of x as a computer:
\(7x + 14 = 14 + 7x\)
7 computers
💻💻💻💻💻💻💻
=
7 computers
💻💻💻💻💻💻💻
✨ 7 computers = 7 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(14 + 7x\) ✓
Question 16
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(5x + 3y + 11\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(5x + 3y + 11\)
⟺
\(11 + 5x + 3y\)
Order of addition doesn't matter
\(5x + 3y + 11 = 11 + 5x + 3y\)
💡 Think of x as a computer:
(With different variables, group each kind separately)
Variable x:
💻💻💻💻💻=💻💻💻💻💻(5x)
Variable y:
📱📱📱=📱📱📱(3y)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(11 + 5x + 3y\) ✓
Question 17
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(x \cdot 9 + 7\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(x \cdot 9 + 7\)
⟺
\(9x + 7\)
Commutative law of multiplication
\(x \cdot a = a \cdot x = ax\)
💡 Think of x as a computer:
\(x \cdot 9 + 7 = 9x + 7\)
1 computers
💻
=
1 computers
💻
✨ 1 computers = 1 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(9x + 7\) ✓
Question 18
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(9x + 3\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(9x + 3\)
⟺
\(3 + 9x\)
Commutative law of addition
\(a + b = b + a\)
Therefore
\(9x + 3 = 3 + 9x\)
💡 Think of x as a computer:
\(9x + 3 = 3 + 9x\)
9 computers
💻💻💻💻💻💻💻💻...
=
9 computers
💻💻💻💻💻💻💻💻💻
✨ 9 computers = 9 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(3 + 9x\) ✓
Question 19
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(3x + 2y + 6\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(3x + 2y + 6\)
⟺
\(6 + 3x + 2y\)
Order of addition doesn't matter
\(3x + 2y + 6 = 6 + 3x + 2y\)
💡 Think of x as a computer:
(With different variables, group each kind separately)
Variable x:
💻💻💻=💻💻💻(3x)
Variable y:
📱📱=📱📱(2y)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(6 + 3x + 2y\) ✓
Question 20
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐
Which expression is equivalent to the following?
\(x \cdot 3 + 5\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(x \cdot 3 + 5\)
⟺
\(3x + 5\)
Commutative law of multiplication
\(x \cdot a = a \cdot x = ax\)
💡 Think of x as a computer:
\(x \cdot 3 + 5 = 3x + 5\)
1 computers
💻
=
1 computers
💻
✨ 1 computers = 1 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(3x + 5\) ✓
Question 21
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(16x + 2\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(16x + 2\)
⟺
\(2(8x + 1)\)
Factor out the common factor
\(16 = 2 \cdot 8\)
Therefore
\(16x + 2 = 2(8x + 1)\)
💡 Think of x as a computer:
\(16x + 2 = 2(8x + 1)\)
16 computers
💻💻💻💻💻💻💻💻...
=
16 computers
💻💻💻💻💻💻💻💻💻💻...
✨ 16 computers = 16 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(2(8x + 1)\) ✓
Question 22
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(6x + 6y\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(6x + 6y\)
⟺
\(6(x + y)\)
Factor out the common factor
\(6x + 6y = 6(x + y)\)
💡 Think of x as a computer:
(With different variables, group each kind separately)
Variable x:
💻💻💻💻💻💻=💻💻💻💻💻💻(6x)
Variable y:
📱📱📱📱📱📱=📱📱📱📱📱📱(6y)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(6(x + y)\) ✓
Question 23
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(4x^{2} + 36x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(4x^{2} + 36x\)
⟺
\(4x(x + 9)\)
Factor out the common ax
\(4x^{2} + 36x = 4x(x + 9)\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(4x(x + 9)\) ✓
Question 24
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(48x + 6\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(48x + 6\)
⟺
\(6(8x + 1)\)
Factor out the common factor
\(48 = 6 \cdot 8\)
Therefore
\(48x + 6 = 6(8x + 1)\)
💡 Think of x as a computer:
\(48x + 6 = 6(8x + 1)\)
48 computers
💻💻💻💻💻💻💻💻...
=
48 computers
💻💻💻💻💻💻💻💻💻💻...
✨ 48 computers = 48 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(6(8x + 1)\) ✓
Question 25
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(11x + 11y\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(11x + 11y\)
⟺
\(11(x + y)\)
Factor out the common factor
\(11x + 11y = 11(x + y)\)
💡 Think of x as a computer:
(With different variables, group each kind separately)
Variable x:
💻💻💻💻💻💻(11)=💻💻💻💻💻💻(11x)
Variable y:
📱📱📱📱📱📱(11)=📱📱📱📱📱📱(11y)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(11(x + y)\) ✓
Question 26
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(5x^{2} + 35x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(5x^{2} + 35x\)
⟺
\(5x(x + 7)\)
Factor out the common ax
\(5x^{2} + 35x = 5x(x + 7)\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(5x(x + 7)\) ✓
Question 27
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(36x + 4\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(36x + 4\)
⟺
\(4(9x + 1)\)
Factor out the common factor
\(36 = 4 \cdot 9\)
Therefore
\(36x + 4 = 4(9x + 1)\)
💡 Think of x as a computer:
\(36x + 4 = 4(9x + 1)\)
36 computers
💻💻💻💻💻💻💻💻...
=
36 computers
💻💻💻💻💻💻💻💻💻💻...
✨ 36 computers = 36 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(4(9x + 1)\) ✓
Question 28
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(8x + 8y\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(8x + 8y\)
⟺
\(8(x + y)\)
Factor out the common factor
\(8x + 8y = 8(x + y)\)
💡 Think of x as a computer:
(With different variables, group each kind separately)
Variable x:
💻💻💻💻💻💻(8)=💻💻💻💻💻💻(8x)
Variable y:
📱📱📱📱📱📱(8)=📱📱📱📱📱📱(8y)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(8(x + y)\) ✓
Question 29
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(4x^{2} + 24x\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(4x^{2} + 24x\)
⟺
\(4x(x + 6)\)
Factor out the common ax
\(4x^{2} + 24x = 4x(x + 6)\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(4x(x + 6)\) ✓
Question 30
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐
Which expression is equivalent to the following?
\(80x + 8\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(80x + 8\)
⟺
\(8(10x + 1)\)
Factor out the common factor
\(80 = 8 \cdot 10\)
Therefore
\(80x + 8 = 8(10x + 1)\)
💡 Think of x as a computer:
\(80x + 8 = 8(10x + 1)\)
80 computers
💻💻💻💻💻💻💻💻...
=
80 computers
💻💻💻💻💻💻💻💻💻💻...
✨ 80 computers = 80 computers
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(8(10x + 1)\) ✓
Question 31
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\(x^{2} - 81\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(x^{2} - 81\)
⟺
\((x + 9)(x - 9)\)
Identify a difference of squares
\(x^{2} - 81 = x^{2} - 9^2\)
Factor
\(= (x + 9)(x - 9)\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \((x + 9)(x - 9)\) ✓
Question 32
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\((x + 6)^2\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\((x + 6)^2\)
⟺
\(x^{2} + 12x + 36\)
Special product formula
\((a+b)^2 = a^2 + 2ab + b^2\)
a = x, b = 6
\(x^{2} + 2 \cdot x \cdot 6 + 6^2\)
Compute
\(= x^{2} + 12x + 36\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(x^{2} + 12x + 36\) ✓
Question 33
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\((x - 9)^2\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\((x - 9)^2\)
⟺
\(x^{2} - 18x + 81\)
Special product formula
\((a-b)^2 = a^2 - 2ab + b^2\)
Compute
\(= x^{2} - 18x + 81\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(x^{2} - 18x + 81\) ✓
Question 34
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\((x + 7)(x - 7)\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\((x + 7)(x - 7)\)
⟺
\(x^{2} - 49\)
Difference of squares formula
\((a+b)(a-b) = a^2 - b^2\)
Compute
\(= x^{2} - 7^2 = x^{2} - 49\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(x^{2} - 49\) ✓
Question 35
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\(x^{2} - 36\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(x^{2} - 36\)
⟺
\((x + 6)(x - 6)\)
Identify a difference of squares
\(x^{2} - 36 = x^{2} - 6^2\)
Factor
\(= (x + 6)(x - 6)\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \((x + 6)(x - 6)\) ✓
Question 36
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\((x + 4)^2\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\((x + 4)^2\)
⟺
\(x^{2} + 8x + 16\)
Special product formula
\((a+b)^2 = a^2 + 2ab + b^2\)
a = x, b = 4
\(x^{2} + 2 \cdot x \cdot 4 + 4^2\)
Compute
\(= x^{2} + 8x + 16\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(x^{2} + 8x + 16\) ✓
Question 37
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\((x - 5)^2\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\((x - 5)^2\)
⟺
\(x^{2} - 10x + 25\)
Special product formula
\((a-b)^2 = a^2 - 2ab + b^2\)
Compute
\(= x^{2} - 10x + 25\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(x^{2} - 10x + 25\) ✓
Question 38
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\((x + 3)(x - 3)\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\((x + 3)(x - 3)\)
⟺
\(x^{2} - 9\)
Difference of squares formula
\((a+b)(a-b) = a^2 - b^2\)
Compute
\(= x^{2} - 3^2 = x^{2} - 9\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(x^{2} - 9\) ✓
Question 39
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\(x^{2} - 121\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\(x^{2} - 121\)
⟺
\((x + 11)(x - 11)\)
Identify a difference of squares
\(x^{2} - 121 = x^{2} - 11^2\)
Factor
\(= (x + 11)(x - 11)\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \((x + 11)(x - 11)\) ✓
Question 40
2.50 pts
🔄 Identifying Equivalent Expressions ⭐⭐⭐⭐
Which expression is equivalent to the following?
\((x + 3)^2\)
💡 Equivalent expressions = give the same result for every value of x
Explanation:
🎉 Solution - Equivalent Expressions
📐 Rule: Equivalent expressions = you can transform one to the other using algebraic operations
\((x + 3)^2\)
⟺
\(x^{2} + 6x + 9\)
Special product formula
\((a+b)^2 = a^2 + 2ab + b^2\)
a = x, b = 3
\(x^{2} + 2 \cdot x \cdot 3 + 3^2\)
Compute
\(= x^{2} + 6x + 9\)
🔍 Check: substitute \(x=2\) in both expressions and verify the same result
Answer: \(x^{2} + 6x + 9\) ✓