Help Factorize and explain please

Question

(x+3)^3(x-1)^2+2(x+3)^2(x-1)^3

Answer 1

(x+3)³(x-1)²+2(x+3)²(x-1)³

1. (x+3)²⁺¹(x-1)²+2(x+3)²(x-1)²⁺¹ Find common factors that appear in all terms. Here we have (x+3) and (x-1) appearing in both terms.
2. (x+3)²(x-1)² ((x+3) + 2(x-1)) Factor out lowest powers of those terms, (x+3)² and (x-1)². Leave remaining factors in parentheses. You can double check if you did this step right by distributing factors now outside the parentheses back inside - you should get the original expression.
3. (x+3)²(x-1)² (3x+1) Simplify insides of the parentheses if possible by adding common terms.
4. Done. The expression is fully factorized when it is written as a product of factors. Note that some expressions can not be fully factorized with real numbers.

Answer 2

First use the distributive law to factor out (x+3)²:

(x+3)²[(x+3)(x-1)² + 2(x-1)³]

Now factor out (x-1)²:

(x+3)²(x-1)²[(x+3)+2(x-1)] = (x+3)²(x-1)²[x+3+2x-2] = (x+3)²(x-1)²(3x+1)