Question

Simplify the expression.

(3(x + 4)^2(x - 7)^2 - (x + 4)^3(2)(x - 7))/(x - 7)^4

Answer 1

[3(x + 4)²(x - 7)² - (x + 4)³2(x - 7)] / (x - 7)⁴

Take out common factors (x + 4)² and (x - 7)

(x + 4)²(x - 7)[3(x - 7) - (x + 4)2]/(x - 7)⁴

Cancel common term.

(x + 4)²[3(x - 7) - (x + 4)2]/(x - 7)³

Distribute terms using distributive property:  a( b + c) = ab + ac

(x + 4)²[3x - 21 - 2x - 8]/(x - 7)³

(x + 4)²[x - 29]/(x - 7)³