Recognizing Products Examples Page 1

Factor the polynomial 3y⁴ - 27x².

This one's trying to fool you, because the polynomial almost looks like a difference of two squares, but it isn't. How dare it try to pull the wool over our eyes? Doesn't it know it's an open weave anyway?

First, we pull out a common factor to get

3(y² - 9x²).

The part in parentheses is a difference of two squares, so it can be written as

(y + 3x)(y - 3x).

To arrive at the final answer, we need to remember to replace the 3 we pulled out. Like you need to remember to replace the roll of toilet paper unless you want your mother screaming at you. Like so:

3(y + 3x)(y - 3x).