# How do you factor 20r^4-45n^4?

Feb 27, 2017

We can factor this using the following rule:

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

Let ${a}^{2} = 20 {r}^{4}$ therefore $\sqrt{{a}^{2}} = a = \sqrt{20 {r}^{4}} = \sqrt{20} {r}^{2}$

Let ${b}^{2} = 45 {n}^{4}$ therefore $\sqrt{{b}^{2}} = b = \sqrt{45 {n}^{4}} = \sqrt{45} {n}^{2}$

Substituting gives:

$20 {r}^{4} - 45 {n}^{4} = \left(\sqrt{20} {r}^{2} - \sqrt{45} {n}^{2}\right) \left(\sqrt{20} {r}^{2} + \sqrt{45} {n}^{2}\right)$