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.

3(y^{2} – 9x^{2})

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)

Example 2

Factor the polynomial 8x^{2} – 56x + 98.

The terms have a common factor of 2, so the first thing we do is pull that out.

2(4x^{2} – 28x + 49)

Now we need to factor the part in parentheses if possible. Since the middle term has a negative sign, we hope we can factor this part like so:

▲^{2} – ■^{2}

Since ▲^{2} = 4x^{2} and ■^{2} = 49, we need ▲ = 2x and ■ = 7.

Squaring (2x – 7) does give us 4x^{2} – 28x + 49, so we can factor the original polynomial as:

2(2x – 7)^{2}

This result was so much more satisfying than that of the last example. Like the last bite of a slice of banana cream pie. Actually, more like the first bite, because then there are still all those other bites left.