Answer
$5x(x+3)(x-3)$
Work Step by Step
We are given the expression $5x^{3}-45x$. First, we can use the distributive property to factor out $5x$, the greatest common factor of both terms.
$5x^{3}-45x=5x(x^{2}-9)$
If $a$ and $b$ are real numbers, we know that $a^{2}-b^{2}=(a+b)(a-b)$.
Therefore, $5x(x^{2}-9)=5x(x+3)(x-3)$.
In this case, $a=x$ and $b=3$.
