Question

factor completely.
$25q^{2}r - 50q^{2} - 20qr + 40q$

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms:
$(25q^{2}r - 50q^{2})+(-20qr + 40q)$

Step2: Factor out GCF from each group

Factor out $25q^{2}$ from the first group and $- 20q$ from the second group:
$25q^{2}(r - 2)-20q(r - 2)$

Step3: Factor out the common binomial factor

Now, factor out the common binomial factor $(r - 2)$:
$(r - 2)(25q^{2}-20q)$

Step4: Factor out GCF from the second binomial

Factor out $5q$ from $25q^{2}-20q$:
$(r - 2)\times5q(5q - 4)$
Which can be written as $5q(5q - 4)(r - 2)$

Answer:

$5q(5q - 4)(r - 2)$