Question

How do you factor `4x^2-4x+1`?

Answer 1

This is a perfect square trinomial:

`4x^2-4x+1 = (2x-1)^2`

Explanation:

One way of quickly spotting this (and a few more) factorisations is the pattern: `4, 4, 1`. The number `441` is the square of `21`, with no carried digits.

Hence we find:

`4x^2+4x+1 = (2x+1)^2`

and:

`4x^2-4x+1 = (2x-1)^2`