# How do you factor completely: 100x^2 – 1?

Jul 29, 2015

color(blue)((10x-1)(10x+1)

#### Explanation:

color(blue)(a^2-b^2 = (a-b)(a+b)

The same property can be applied for the above expression:

$100 {x}^{2} - 1$, here color(blue)(a=10x, b=1

The expression can now be factorised as:
100x^2-1 = (10x)^2 - 1^2 = color(blue)((10x-1)(10x+1)