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We need to factor 49x squared minus 49y squared.

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Now here there's a pattern that you might already be

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familiar with.

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But just to make sure you are, let's think about what happens

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if we multiply a plus b-- where these are just two terms

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in a binomial-- times a minus b.

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If you multiply this out, you have a times a, which is a

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squared, plus a times negative b, which is negative ab--

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that's a times negative b-- plus b times a, which is the

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same thing as ab.

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And then you have b times negative b, which

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is negative b squared.

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So when you do that, you have a negative ab and a positive

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ab, they cancel out.

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And you're just going to be left with an a

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squared minus a b squared.

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Now, this thing that we have here is exactly that pattern.

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49x squared is a perfect square.

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49y squared is a perfect square.

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We can rewrite it like that.

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We could rewrite this over here as 7x squared minus-- and

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I'll do it in blue-- minus 7y squared.

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And so you see it's a pattern.

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It's a squared minus b squared.

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So if you wanted to factor this-- if you would just use

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this pattern that we just derived-- you would say that

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this is the same thing as a, 7x plus b plus 7y times 7x

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minus b, minus 7y.

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And you'd be done.

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Now there's one alternate way that you could factor this and

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it'd be completely legitimate.

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You could start from the beginning and

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say, you know what?

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49 is a common factor here, so let me just factor that out.

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So you could say it's equivalent to 49 times x

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squared minus y squared.

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And you say, oh, this fits the pattern of-- this is a squared

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minus b squared.

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So this will be x plus y times x minus y.

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So the whole thing would be 49 times x plus y

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times x minus y.

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And to see that this, right here, is the exact same thing

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as this right over here, you could just factor 7 out of

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both of these.

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You'd factor out a 7 out of that term, a factor

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7 out of that term.

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And when you multiply them, you'd get the 49.

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So these are-- this or this-- these are both ways to factor

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this expression.

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