# How do you factor: y=x^2 - 5?

Dec 23, 2015

Apply the difference of squares formula to find that
${x}^{2} - 5 = \left(x + \sqrt{5}\right) \left(x - \sqrt{5}\right)$

#### Explanation:

The difference of squares formula states that
${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$
(This is easy to verify by expanding the right hand side)

While $5$ may not be a perfect square, it is still the square of something... specifically, it is the square of $\sqrt{5}$
Then, applying the formula, we have

${x}^{2} - 5 = {x}^{2} - {\left(\sqrt{5}\right)}^{2} = \left(x + \sqrt{5}\right) \left(x - \sqrt{5}\right)$