# How do you factor 1/25h^2-16=0?

May 9, 2015

To eliminate the fraction, we can multiply both sides of the equation by 25

$25 \left(\frac{1}{25} {h}^{2} - 16\right) = 25 \cdot 0$

$\to {h}^{2} - 25 \cdot 16 = 0$

$\to {h}^{2} - {5}^{2} \cdot {4}^{2} = 0$

$\to {h}^{2} - {\left(5 \cdot 4\right)}^{2} = 0$

$\to {h}^{2} - {20}^{2} = 0$

We know the Difference of Squares Identity which says:
color(blue)(a^2 - b^2 = (a+b)(a-b)

Applying it to the equation, we get:

-> color(green)((h+20)(h-20) = 0

This tells us that either $h + 20 = 0$ or $h - 20 = 0$

color(green)(h = -20 or h = 20