Question

How do you use the difference of two squares formula to factor `4(x + 2)² - 36`?

Answer 1

The difference of two square formula says that `a^2+b^2=(a+b)(a-b)`

Let's call `P(x)=4(x+2)^2-36`
So here:

`a=2(x+2)`
`b=6`

So `P(x)=(2(x+2)+6)(2(x+2)-6)`, and it's a prime factorisation because the two factors are polynomials of degree 1, which are always irreducible.

So the answer is (if you write `2` outside the brackets)

`P(x)=4(x+2+3)(x+2-3)=4(x+5)(x-1)`