Simplifying Algebraic Expressions Using the Distributive Property

Match the following expressions to the correct simplified response.

• -9x + 18

• 1/2(-b + 4)

• 100 + 30x

• 0.5(16a - 16)

• -1/2b + 2

• -3(3x - 6)

• 8a - 8

• -10(-10 - 3x)

• 2n - 10

• (n - 5)2

What does the distributive property allow us to do in algebraic expressions?

• Combine like terms

• Remove parentheses

• Solve equations

• Factor polynomials

What does the presence of parentheses in an algebraic expression usually indicate?

• Subtraction

• Addition

• Multiplication

• Division

Which of the following is a correct application of the distributive property?

• a(b + c) = ab + ac

• a + b + c = a(b + c)

• a(b - c) = ab - ac

• Both a(b + c) = ab + ac and a(b - c) = ab - ac

What is the result of distributing 9 to the expression 3C + 2?

• 12C + 11

• 9C + 11

• 27C + 18

• 27C + 2

How do we treat the subtraction sign when distributing a coefficient to terms inside parentheses?

• Ignore it

• Treat it as addition

• Include it with the term following it

• Convert it to multiplication

What is the simplified form of 4(-6y - 5)?

• -24y + 20

• 24y - 20

• -30y

• -24y - 20

When simplifying expressions with negative coefficients, what happens when you multiply two negatives?

• It becomes subtraction

• It remains negative

• It becomes division

• It becomes positive

In the expression -2(-8x - 7y), what is the simplified form?

• -16x - 14y

• 16x - 14y

• -16x + 14y

• 16x + 14y

How can double signs be simplified in algebraic expressions?

• By converting them to multiplication

• By ignoring one of the signs

• By converting subtraction of a negative to addition

• By leaving them as is for clarity