Factoring difference of squares: two variables (example 2)

we two-factor 49 x squared - 49 y squared now here there's a a pattern that might you might already be familiar with but just to make sure you are let's think about what happens if we multiply a plus B where these are just two terms in a binomial times a minus B if you multiply this out you have a times a which is a squared plus a times negative B which is negative a B that's a times negative B plus B times a which is the same thing as a B and then you have B times negative B which is negative B squared so when you do that you have a negative a B and a positive a B they cancel out and you're just going to be left with an a squared minus a B squared now this thing that we have here is exactly that pattern 49 x squared is a perfect square 49 y squared is a perfect square we can rewrite it like that 49 we could rewrite this over here as 7x squared - mile do it in blue - 7y squared and so you see it's a pattern it's a squared - B squared so if you wanted to factor this if you just use this pattern that we just I guess you say derived you would say that this is the same thing as a 7x plus b plus 7y times 7x times 7x minus b minus 7y and you'd be done now there's one alternate way that you could factor this it would be completely legitimate you could start from the beginning and say you know what forty-nine is a common factor here so let me just factor that out so you could say it's equivalent to 49 times x squared minus y squared and you say oh this fits the pattern of a plot this is a be a squared minus B squared this is so this will be X plus y times X minus y so the whole thing would be 49 times X plus y times X minus y and to see that this right here is the exact same thing as this right over here you could just factor seven out of both of these you'd factor out a 7 out of that term a factor 7 out of that term when you multiply them you'd get the 49 so these are this or this these are both ways to factor this expression