Question

How do you factor `x^2-16` completely?

Answer 1

`=(x+4)(x-4)`

Explanation:

`a^2-b^2=(a+b)(a-b)`

Similarly `x^2-16`

`=(x^2-4^2)`

`=(x+4)(x-4)`

Answer 2

`x^2-16=(x+4)(x-4)`

Explanation:

There are two ways to factorize `x^2-16` - one using identity `a^2-b^2=(a+b)(a-b)`.

As such `x^2-16=x^2-4^2`

= `(x+4)(x-4)`

Other method is by splitting the middle term, which is `0` here and as product of coefficient of `x^2` and constant term is `-16`. we need to do is to split middle term in `4` and `-4` (as their sum is zero and product is `-16`).

Hence `x^2-16`

= `x^2-4x+4x-16`

= `x(x-4)+4(x-4)`

= `(x+4)(x-4)`