Question

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

Answer 1

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

Explanation:

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