Question

How to factorise `4x^2+4x-1`?

Answer 1

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

Explanation:

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

`A^2-B^2 = (A-B)(A+B)`

with `A=(2x+1)` and `B=sqrt(2)` as follows:

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

`color(white)(4x^2+4x-1) = (2x+1)^2-(sqrt(2))^2`

`color(white)(4x^2+4x-1) = ((2x+1)-sqrt(2))((2x+1)+sqrt(2))`

`color(white)(4x^2+4x-1) = (2x+1-sqrt(2))(2x+1+sqrt(2))`