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Current time:0:00Total duration:5:10

Video transcript

what we're going to do in this video is practice squaring binomials and this is something that we've done in the past but we're gonna do it with slightly more involved expressions but let's just start with a little bit of review if I were to ask you what is a plus B squared what would that be pause the video and try to figure it out well some of you might immediately know what a binomial like this squared is but I'll work it out so this is the same thing as a plus B times a plus B and then we could multiply this a times that a so that's going to give us a squared and then I can multiply that a times that B and that's going to give us a B then I could multiply this B times that a I could write that as B A or a B so I'll just write it as a B again and then I multiplied this B times that be so plus B squared and what I really just did is applied the distributive property twice we go into a lot of detail in previous videos some people also like to call it the foil method either way this should all be a review if it's not I encourage you to look at those introductory videos but this is going to simplify to a squared plus we have an a B and another a B so you add those together you get to a b plus b squared now why did i go through this review well now we can use this idea that a plus B squared is equal to a squared plus 2a B plus B squared to tackle things that at least look a little bit more involved so if I were to ask you what is 5 X to the sixth plus 4 squared pause this video and try to figure it out and try to keep this and this in mind well there's several ways you could approach this you could just expand this out the way we just did or you could recognize this pattern that we just established that if I have an A plus B and I squared it's going to be this and so what you might notice is the role of a is being played by five X to the sixth right over there and the role of B is being played by four right over there so we could say hey this is going to be equal to a squared we have our a squared there so what is a squared well five X to the sixth squared is going to be 25 of X to the 12th power and then it's going to be plus two times a times B so plus two times five x to the sixth times four actually let me just write it out just so we don't confuse ourselves two times five x to the I'll color code it to two times five x to the sixth times four times four plus B squared so plus four squared so that's going to be plus sixteen and then we can simplify this so this is going to be equal to 25 X to the twelfth two times five times four is forty two times five is ten times 4 is 40 so plus 40 X to the sixth plus 16 let's do another example and I'll do this one even a little bit faster just because we're getting I think pretty good at this so let's say we're trying to determine what 3t squared minus 7t to the sixth power squared is pause the video and try to figure it out all right we're going to do it together now so this is our a and our B now we should view as negative seven T to the sixth because it says plus B so you could view this as plus negative seven T to the sixth we could even write that if we want we could write this plus negative 72 the six if it helps us recognize this whole thing is B so this is going to be equal to a squared which is nine t to the fourth plus two times this times this two times a times B so two times 3t squared is going to be six T squared times negative seven T to the sixth actually let me write this out this is getting a little bit complicated so this is going to be plus two times 3t squared times negative seven T to the sixth power and then last but not least we are going to square negative seven T to the six so that's going to be negative 7 squared is positive 49 and T to the sixth squared is T to the twelfth to the 12th power and so this is going to be equal to 9 t to the 4th and let's see 2 times 3 is 6 times negative 7 is negative 42 and T squared times T to the sixth we add the exponents we have the same base so it's going to be T to the 8th and then we have plus 49 T to the 12th power so it looks like we did something really fancy we have this higher degree polynomial we were squaring this binomial that has these higher degree terms but we're really just applying the same idea that we learned many many many videos ago many many lessons ago in terms of just squaring binomials