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# Special products of binomials: two variables

CCSS.Math:

## Video transcript

find the area of a square with side six X minus five Y so let me draw our square and all of the sides of a square we're going to have the same lengths and they're telling us that the length for each of the sides which is the same for all of them is 6x minus 5y so the height would be 6x minus 5y and so with the width 6x minus 5y and if we wanted to find the area of the square we just have to multiply the width times the height so the area for this square is just going to be the width which is 6x minus 5y times the height times the height which is also 6x minus 5y so we just have to multiply these two binomials and to do this you could either do foil if you like memorizing things or you can just remember this is just applying the distributive property twice so we could do is distribute this entire magenta 6x minus 5y times each of distribute it over each of these terms in the yellow 6x minus 5y and if we do that we will get this 6x this six x times this entire 6x minus 5y so 6x minus 5y and then we have minus 5y minus 5y times once again the entire magenta 6x minus 5y and what does this give us so we have we have 6x times 6x so the when I distribute it just this where I'm now doing the distributive property for the second time 6x times 6x is 36 x squared and then when I take 6x and then when I take 6x times negative 5y I get 6 times negative 5 is negative 30 and then I have an x times y negative 30 X Y and then I want to take and then I want to take I'm trying to introduce many colors here so I have this negative 5y times this 6x right over here so negative 5 times 6 is negative 30 negative 30 and I have a Y an X or an X and a y and then finally I have my last distribution to do let me do that maybe in white I have five Y times I'll actually have a negative 5y times another negative 5y so the negative times a negative is a positive so it is positive five times five is twenty-five Y times y is y squared and then we are almost we are almost done right over here we could say we can just add these two terms in the middle right over here negative 30 XY minus third 30 XY is going to be negative 60 XY so you get 36 x squared minus 60 XY plus 25y squared now there is a faster way to do this if you recognize if you recognize that if I'm squaring a binomial which is essentially what we're doing here this is the exact same thing as 6x minus 5y squared so you might recognize the pattern if I have a plus B squared this is the same thing as a plus B times a plus B and if you were to multiply it out this exact same way we just did it here the pattern here is it's a times a which is a squared plus a times B plus a B plus B times a which is also a B if you just switch the order plus B squared plus B squared so this is equal to a squared plus 2 a B plus B squared this is kind of the fast way to look whenever if you're squaring any binomial it'll be a plus B squared will be a squared plus 2 a B plus B squared and if you knew this ahead of time then you could have just applied that to this to the squaring of the binomial right up here so we let's do it that way as well so if we have 6x 6x minus 5y squared we could just say well this is going to be a squared it's going to be a squared in which in this case is 6x squared plus 2 a B so that's plus 2 times a which is 6x times B which is negative 5y negative 5y plus B squared which is plus negative 5y everything squared and then this will simplify to 6 x squared is 36 x squared plus actually there's going to be a negative here because it's going to be 2 times 6 is 12 times negative 5 is negative 60 we have x and a y x and a y and the negative 5y squared is positive 25 y squared so hopefully you saw multiple ways to do this if you saw this pattern immediately and if you knew this pattern immediately you could just cut to the chase and go straight here you wouldn't have to do the distributive property twice although this will never be wrong