# How do you factor 64-y^2?

Jun 18, 2015

#### Answer:

Here's the result: $\left(8 - y\right) \left(8 + y\right)$

#### Explanation:

Start off by appreciating the fact that: $\left(a - b\right) \left(a + b\right) = {a}^{2} + \textcolor{red}{a b - a b} - {b}^{2}$
$\implies \left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$

So, generally ${a}^{2} - {b}^{2} = \left(\sqrt{{a}^{2}} - \sqrt{{b}^{2}}\right) \left(\sqrt{{a}^{2}} + \sqrt{{b}^{2}}\right)$

Therefore, in our present situation,
$\left(64 - {y}^{2}\right)$ by comparing with the above results,
$64 - {y}^{2} = = \left(\sqrt{64} - \sqrt{{y}^{2}}\right) \left(\sqrt{64} + \sqrt{{y}^{2}}\right) = \left(8 - y\right) \left(8 + y\right)$

That's it!