# How do you factor 1 - 100x^2?

Dec 29, 2015

Use difference of squares to factorize this. The method is given below.

#### Explanation:

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

Now let us take up our problem

$1 - 100 {x}^{2}$

Ask can we write this expression in ${a}^{2} - {b}^{2}$ form.

$1 i s s a m e a s {1}^{2}$
$100$ can be written as ${10}^{2}$

So, we have $1 - 100 {x}^{2}$ as ${1}^{2} - {10}^{2} {x}^{2}$

If ${10}^{2} {x}^{2}$ is putting you off, it is nothing but ${\left(10 x\right)}^{2}$

Rule $\left({a}^{m} {b}^{m}\right) = {\left(a b\right)}^{m}$

Now our expression becomes
${1}^{2} - {\left(10 x\right)}^{2}$

This can be factored by the difference of squares.

${1}^{2} - {\left(10 x\right)}^{2} = \left(1 - 10 x\right) \left(1 + 10 x\right)$ Answer