Answer
$(5x)(25x^2+15x+3)$
Work Step by Step
With $1=1^3$, the given expression is equivalent to:
$=(5x+1)^3-1^3$
RECALL:
The difference of two cubes $a^3-b^3$ can be factored using the formula:
$a^3-b^3=(a-b)(a^2+ab+b^2)$
Factor the given difference of two cubes using the formula above with $a=5x+1$ and $b=1$ to obtain:
$(5x+1)^3-1^3
\\=[(5x+1)-1][(5x+1)^2+(5x+1)(1)+1^2]
\\=(5x+1-1)[(25x^2+2(5x)(1)+1^2)+(5x+1)+1]
\\=(5x)[25x^2+10x+1+5x+1+1]$
Combine like terms to obtain:
$=(5x)[25x^2+(10x+5x)+(1+1+1)]
\\=(5x)(25x^2+15x+3)$
