Factoring and Expanding Expressions

Multiple Choice

What is the equivalent expression for: $$\frac {\text{-}1}{4}(-8x+12y)$$ ?

• 2x + 3y
• 2x - 3y
• -2x - 3y
• -2x + 3y

Multiple Choice

Factor to write an equivalent expression: $$36a-16$$

• 4(9a + 4)
• 2(18a - 8)
• 6(6a - 2)
• 4(9a - 4)

Open Ended

Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin understands that expanding is using the distributive property, but she doesn’t understand what factoring is or why it works. How can Kiran explain factoring to Lin?

Multiple Choice

What should Kiran tell Lin about the boxes used in diagrams for factoring?

• The boxes represent the terms of the polynomial and help visualize the factoring process.
• The boxes are irrelevant to the factoring process.
• The boxes indicate the degree of the polynomial.
• The boxes are used to represent the coefficients only.

Multiple Choice

Lin missed math class on the day they worked on expanding and factoring. Kiran is helping Lin catch up. Lin asks Kiran to help her factor the expression $$-4xy-12xz+20xw$$ . What is the factored form of the expression?

• -4(y + 3z - 5w)
• -4(-y - 3z + 5w)
• -4(2y + 6z - 10w)
• -4(y - 3z + 5w)

Multiple Choice

Complete the equation with numbers that make the expression on the right side of the equal sign equivalent to the expression on the left side. $$75a + 25b = \underline{\ \ \ \ }( \underline{\ \ \ \ }a + b)$$

• 25, 3

• 15, 5

• 50, 2

• 100, 1

Multiple Choice

Factor the expression: $$15a-13a$$ .

• -13a
• 2a
• 15a
• 3a

Multiple Choice

Factor the expression: $$-6x-18y$$ .

• -3(2x + 6y)
• -6(x - 3y)
• -2(3x + 9y)
• -6(x + 3y)

Multiple Choice

What is the factored form of the expression: $$36abc+54ad$$ ?

• 18b(2ac + 3d)
• 9a(4bc + 6d)
• 36a(1bc + 1.5d)
• 18a(2bc + 3d)

Multiple Select

Select **all** the expressions that are equivalent to $$-36x+54y-90$$ .

• $$-9(4x-6y-10)$$

• $$-2(18x-27y+45)$$

• $$-6(6x+9y-15)$$

• $$18(-2x+3y-5)$$

• $$-18(2x-3y+5)$$