Simplifying $3x^2(x+8)^3+3x^3(x+8)^2$

Question

I found the derivative of $[x^3(x+8)^3]$ to equal $3x^2(x+8)^3+3x^3(x+8)^2$ using Chain Rule.

Somehow it can simplify further to: $6x^2(x+4)(x+8)^2$.

I can't manage the steps to get it to the simplified form.

Answer 1

Carry out continuous factorizations, as :

$$3x^2(x+8)^3+3x^3(x+8)^2 = 3x^2\Big[(x+8)^3+x(x+8)^2\Big] $$ $$=$$ $$3x^2(x+8)^2\Big[x+8 + x\Big] = 3x^2(x+8)^2(2x+8) $$ $$=$$ $$\boxed{6x^2(x+4)(x+8)^2}$$