Question

factor $-16n^4 + 100$ completely.
$-16n^4 + 100 = \square$

Explanation:

Step1: Factor out GCF

First, factor out the greatest common factor of -4 from both terms.
$-16n^4 + 100 = -4(4n^4 - 25)$

Step2: Recognize difference of squares

Notice that $4n^4 - 25$ is a difference of squares, where $4n^4=(2n^2)^2$ and $25=5^2$. Use the difference of squares formula $a^2 - b^2=(a-b)(a+b)$.
$4n^4 - 25 = (2n^2 - 5)(2n^2 + 5)$

Step3: Combine factors

Substitute the factored form back into the expression from Step1.
$-4(4n^4 - 25) = -4(2n^2 - 5)(2n^2 + 5)$

Answer:

$-4(2n^2 - 5)(2n^2 + 5)$