Question

20) Use the distributive property to factor the expression. 10xz − 20yz A) z(10x − 20y) B) 10(xz − 2yz) C) 10z(x − 2y) D) xyz(10 − 20)

Answer 1

C. 10z(x - 2y)

Explanation:

10xz − 20y

Factor the terms

Factors of 10xz = 2 × 5 × x × z

Factors of -20yz = (-1) × 2 × 2 × 5 × y × z

Identify their greatest common factor

The common factors are 2, 5, and z. The greatest common factor is 10z.

Rewrite them with the GCF as a factor

10xz = 10z × x

-20yz = 10z × (-2y)

Replace the terms in the original expression with the factored terms

10xz − 20yz = 10z(x) + 10z(-2y)

Use the distributive property to isolate the greatest common factor

10z(x) + 10z(-2y) = 10z(x - 2y)