# How do you use the difference of two squares formula to factor x^2-4?

May 4, 2015

Factor ${x}^{2} - 4$ using the difference of two squares.

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

$\left({x}^{2} - 4\right) = \left({x}^{2} - {2}^{2}\right) = \left(x - 2\right) \left(x + 2\right)$

May 4, 2015

So the difference of 2 squares formula says that $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

In this case, $a = \sqrt{1}$ and $b = \sqrt{4}$ (we get this from ${x}^{2} - 4$)

So, $a = 1$ and b=±2

Therefore, ${x}^{2} - 4 = \left(x + 2\right) \left(x - 2\right)$