Factor by Grouping 4k^5-100k^3

$4 k^{5} - 100 k^{3}$

Factor out the GCF of $4 k^{3}$ from $4 k^{5} - 100 k^{3}$ .

Factor out the GCF of $4 k^{3}$ from each term in the polynomial.

Factor out the GCF of $4 k^{3}$ from the expression $4 k^{5}$ .

$4 k^{3} (k^{2}) - 100 k^{3}$

Factor out the GCF of $4 k^{3}$ from the expression $- 100 k^{3}$ .

$4 k^{3} (k^{2}) + 4 k^{3} (- 25)$

Since all the terms share a common factor of $4 k^{3}$ , it can be factored out of each term.

$4 k^{3} (k^{2} - 25)$

Rewrite $25$ as $5^{2}$ .

$4 k^{3} (k^{2} - 5^{2})$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = k$ and $b = 5$ .

$4 k^{3} ((k + 5) (k - 5))$