How to factor

Question

(x+2)³ (x-3)⁵ +(x-3)⁶ (x+2)²

I do not understand how i would break down and factor this problem

Answer 1

(x + 2)³(x - 3)⁵ + (x - 3)⁶(x + 2)²

(x + 2)²[(x + 2)(x - 3)⁵ + (x - 3)⁶]   factor out (x + 2)²

(x + 2)²(x - 3)⁵[(x + 2) + (x - 3)]     factor out (x - 3)⁵

(x + 2)²(x - 3)⁵(2x - 1)                   combine like terms

Answer 2

Examine all terms (there are two terms, separated by the plus sign in the middle of the expression).

 

In the first term there appears the quantity (factor) (x+2) with exponent 3, and the same factor appears in the second term with factor two. Therefore (x+2)² is a common factor.

 

Similarly, (x-3)⁵ is a common factor. Therefore the expression =

(x+2)²(x-3)⁵[(x+2) + (x-3)] and you can simplify the expression in square brackets to get the final answer,

 

(x+2)²(x-3)⁵(2x-1)