Question

How do you factor `x^2-4y^2-4x+4` by grouping?

Answer 1

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

Explanation:

The difference of squares identity can be written:

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

By rearranging the given quadratic, we can recognise it as a difference of squares and hence factor it:

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

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

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

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