Answer
$2(x^{2}+9)(x^{2}-9)$
Work Step by Step
We are given the expression $2x^{4}-162$. First, we can use the distributive property to factor out 2, the greatest common factor of both terms.
$2x^{4}-162=2(x^{4}-81)$
If $a$ and $b$ are real numbers, we know that $a^{2}-b^{2}=(a+b)(a-b)$
Therefore, $2(x^{4}-81)=2(x^{2}+9)(x^{2}-9)$.
In this case, $a=x^{2}$ and $b=9$.
