Answer
$(5x)(25x^2+15x+3)$
Work Step by Step
Write $1$ as $1^3$:
$(5x+1)^3-1=(5x+1)^3-1^3$
Use the special formula $a^3-b^3=(a-b)(a^2+ab+b^2)$ where $a=(5x+1)$ and $b=1$.
$=[(5x+1)-1][(5x+1)^2+(5x+1)(1)+1^2]$
Simplify.
$=(5x)[(5x+1)^2+5x+1+1]$
$=(5x)[(5x+1)^2+5x+2]$
Use the special formula $(a+b)^2=a^2+2ab+b^2$ where $a=5x$ and $b=1$.
$=(5x)[(5x)^2+2(5x)(1)+(1)^2+5x+2]$
Simplify.
$=(5x)[25x^2+10x+1+5x+2]$
$=(5x)(25x^2+15x+3)$
Hence, the completely factored form of the given expression is $(5x)(25x^2+15x+3)$.
