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

Answer:

C. 10z(x - 2y)

Step-by-step 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)