Question

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

Answer 1

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

Explanation:

This polynomial is a perfect square of the type `a^2+2ab+b^2`,

as `4x^2+4x+1` can be written as

`(2x)^2+2xx2x xx 1+1^2`

with `a=2x` and `b=1`

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

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