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).
Factor the polynomial 8x2 - 56x + 98.
The terms have a common factor of 2, so the first thing we do is pull that out to get
2(4x2 - 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 as
(▲)2 - (■)2.
We would need
▲ = 2x
■ = 7.
Squaring (2x - 7) does give us 4x2 - 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.