Question

How do you factor `x^2-4x-4`?

Answer 1

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

Explanation:

We can factor this by completing the square and using the difference of squares identity:

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

with `a=(x-2)` and `b=2sqrt(2)` as follows:

`x^2-4x-4 = x^2-4x+4-8`

`color(white)(x^2-4x-4) = (x-2)^2-(2sqrt(2))^2`

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

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