Question

How do you factor `x^2-y^2-8x+16` ?

Answer 1

`x^2-y^2-8x+16 = (x-y-4)(x+y-4)`

Explanation:

The difference of squares identity can be written:

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

We can use this with `a=(x-4)` and `b=y` as follows:

`x^2-y^2-8x+16 = (x^2-8x+16)-y^2`

`color(white)(x^2-y^2-8x+16) = (x-4)^2-y^2`

`color(white)(x^2-y^2-8x+16) = ((x-4)-y)((x-4)+y)`

`color(white)(x^2-y^2-8x+16) = (x-y-4)(x+y-4)`