Question

How do you factor the expression `x² - 4x + 4`?

Answer 1

This is a perfect square trinomial:

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

Explanation:

In the general case we have:

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

By reversing the sign on `b` we can also write:

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

So if the first and last terms of a trinomial are both squares, just check that the middle one is `+-` twice the product of the square roots of those terms. If it is then you have a perfect square trinomial.

In our example, `a=x` and `b=-2`, giving:

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