Question

factor: –3b(b–2)+7(b–2)^2

Answer 1

first, (b-2)^2

(a-b)^2 = a^2 - 2 ab + b^2

where a is b (confusing right) and b is 2 so this becomes

b^2 -4b + 4

-3b(b-2) + 7 (b^2 - 4b +4)

distributive property says

-3b^2 + 6b + 7b^2 -28b +28

group like terms

4b^2 -22b + 28

divide out a 2

2(2b^2 - 11b + 14)

factor with 2, 1 being factors of two, and 2, 7 being factors of 14

2 (2b-7)(b-2)