How do you factor w^4-625?

Jun 18, 2018

$\left({w}^{2} + 25\right) \left(w - 5\right) \left(w + 5\right)$

Explanation:

$625 = {5}^{4}$

${w}^{4} - {5}^{4}$, using the difference of two squeares we get:

$\left({w}^{2} + {5}^{2}\right) \left({w}^{2} - {5}^{2}\right)$

And again:
$\left({w}^{2} + 25\right) \left(w - 5\right) \left(w + 5\right)$

Jun 18, 2018

See a solution process below:

Explanation:

First, we can rewrite the expression and factor it as:

${\left({w}^{2}\right)}^{2} - {\left(25\right)}^{2} \implies \left({w}^{2} + 25\right) \left({w}^{2} - 25\right)$

We can then factor the term on the right as:

$\left({w}^{2} + 25\right) \left(w + 5\right) \left(w - 5\right)$

Jun 18, 2018

$\left(w + 5\right) \left(w - 5\right) \left({w}^{2} + 25\right)$

Explanation:

Remember that ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

${w}^{4} - 625$
$= {\left({w}^{2}\right)}^{2} - {25}^{2}$
$= \left({w}^{2} - 25\right) \left({w}^{2} + 25\right)$
$= \left({w}^{2} - {5}^{2}\right) \left({w}^{2} + 25\right)$
$= \left(w + 5\right) \left(w - 5\right) \left({w}^{2} + 25\right)$