Answer
$6(x+5)^3(x-1)(x+1)$
Work Step by Step
The given expression is $4(x+5)^3(x-1)^2+(x+5)^4\cdot 2(x-1)$.
Factor out $2(x+5)^3(x-1)$.
$=2(x+5)^3(x-1)[2(x-1)+(x+5)]$
Use distributive property.
$=2(x+5)^3(x-1)[2x-2+x+5]$
Add like terms.
$=2(x+5)^3(x-1)[3x+3]$
Factor out $3$.
$=2(x+5)^3(x-1)(3)(x+1)$
$=6(x+5)^3(x-1)(x+1)$
Hence, the completely factored form of the given expression is $6(x+5)^3(x-1)(x+1)$.
