# How do you factor 1/4x^2-4?

Apr 9, 2016

$\left(\frac{x}{2} + 2\right) \left(\frac{x}{2} - 2\right)$

#### Explanation:

We will use the following property to find the factors of the given expression:

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

Solution:

$\frac{1}{4} {x}^{2} - 4$

Here, ${a}^{2} = \frac{1}{4} {x}^{2}$ and ${b}^{2} = 4$

$\implies a = \frac{1}{2} x$ and $b = 2$

$\frac{1}{4} {x}^{2} - 4 = \left(\frac{x}{2} + 2\right) \left(\frac{x}{2} - 2\right)$