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## Factoring using structure

Current time:0:00Total duration:1:49

# Factoring using the difference of squares pattern

CCSS.Math:

## Video transcript

Factor x squared
minus 49y squared. So what's interesting
here is that well x squared is clearly
a perfect square. It's the square of x. And 49y squared is
also a perfect square. It's the square of 7y. So it looks like we might
have a special form here. And to remind
ourselves, let's think about what happens if we take
a plus b times a minus b. I'm just doing it
in the general case so we can see a pattern here. So over here, this
would be a times a, which would be a squared
plus a times negative b, which would be negative ab plus
b times a or a times b again, which would be ab. And then you have
b times negative b, so it would b minus b squared. Now these middle two
terms cancel out. Negative ab plus
ab, they cancel out and you're left with just
a squared minus b squared. And that's the exact
pattern we have here. We have an a squared
minus a b squared. So in this case, a is equal
to x and b is equal to 7y. So we have x squared minus
7y, the whole thing squared. So we can expand this as
the difference of squares, or actually this
thing right over here is the difference of squares. So we expand this like this. So this will be equal to x
plus 7y times x minus 7y. And once again,
we're just pattern matching based on this
realization right here. If I take a plus
b times a minus b, I get a difference of squares. This is a difference of squares. So when I factor
it, it must come out to the result of
something that looks like a plus b times a minus b
or x plus 7y times x minus 7y.