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

1 Answer
May 2, 2015

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)