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)#