Algebra Midterm Review

Evaluate y + 6 + y for y = 8

Answer explanation

Substitute 8 for the variable y.

8 + 6 + 8 = 22

3y + 4x = 4x + 3y is an example of which property?

• Commutative Property of Multiplication
• Associative Property of Multiplication
• Commutative Property of Addition
• Associative Property of Addition

Answer explanation

The Commutative Property of Addition lets us move terms around an expression and it remains equivalent.

Evaluate for x = 3

x² – 5

Evaluate for y = 6

(y – 1)²

Answer explanation

Substitute 6 for y
(6 - 1)(6 - 1) = 5(5) = 25

Evaluate for y = 3

(4y)²

Find an equivalent expression using the distributive property. 3(2x + y)

• 5x + y
• 5x + 3y
• 6x + 3y
• 6x + y

Answer explanation

We multiply the first term (2x) by 3, then add 3 multiplied by y.

3(2x) + 3(y) = 6x + 3y

Find an equivalent expression using the distributive property. 4(3x + 4y + z)

• 7x + 8y + 4z
• 12x + 16y + 4z
• 15x + 12y + 7z
• 10x + 8y + 5z

Answer explanation

Multiply every term in the parenthesis by 4
4(3x) + 4(4y) + 4(z) = 12x + 16y + 4z

Collect like terms 7a + 7b + a + 7c

• 8a + 7b + 7c
• 7a + 7b + 7c
• 7a + 8ab + 7c
• 7a² + 7b + 7c

Answer explanation

7a and a are like terms because they have the exact same variable.
The sum of 7a and 1a = 8a

The other terms remain unchanged.

Collect like terms.

6x² + 2y + 2x + 3x²

• 9x² + 2x + 2y

• 9x + 2x + 2y
• 6x²+ 2y + 5x

• 11x + 2y

Which option is the algebraic expression of 7 less than twice x?

• 7 - 2x
• 2x - 7
• 2(7) - 2(x)
• 2 + x - 7

Answer explanation

Beginning at the end, we multiply x by 2. Then we take 7 less than the product of 2x.
2x - 7