Answer
$5(x+3)(x-2)^2(x+1)$
Work Step by Step
The given expression is $2(x+3)(x-2)^3+(x+3)^2\cdot 3(x-2)^2$.
Factor out $(x+3)(x-2)^2$.
$=(x+3)(x-2)^2[2(x-2)+3(x+3)]$
Use distributive property.
$=(x+3)(x-2)^2[2x-4+3x+9]$
Add like terms.
$=(x+3)(x-2)^2(5x+5)$
Factor out $5$.
$=5(x+3)(x-2)^2(x+1)$
Hence, the completely factored form of the given expression is $5(x+3)(x-2)^2(x+1)$.
