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

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Answer 1 · 2015-12-29T13:30:35

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

Difference of squares $a^2 - b^2 = (a-b)(a+b)$

Now let us take up our problem

$1 - 100x^2$

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

$1 is same as 1^2$
$100$ can be written as $10^2$

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

If $10^2x^2$ is putting you off, it is nothing but $(10x)^2$

Rule $(a^mb^m) = (ab)^m$

Now our expression becomes
$1^2 - (10x)^2$

This can be factored by the difference of squares.

$1^2 - (10x)^2 = (1-10x)(1+10x)$ Answer

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