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(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.
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 like so:
▲2 – ■2
Since ▲2 = 4x2 and ■2 = 49, we need ▲ = 2x and ■ = 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.