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Current time:0:00Total duration:2:29

Special products of the form (ax+b)(ax-b)


Video transcript

find the product 2x plus 8 times 2x minus 8 so we're multiplying two binomials so you could use foil you could just straight-up use the distributive property here but the whole point of this problem I'm guessing is to see whether you recognize the pattern here this is of the form a plus B times a minus B where here a is 2x and B is 8 we have 2x Plus 8 and then 2x minus 8 a plus B a minus B what I want to do is I'm just going to multiply this out for us and then just see what happens whenever you have this pattern what the product actually looks like so if you were to multiply this out we can distribute the a plus B we can distribute this whole thing the distribute the whole a plus B on the a and then distribute it on the B and I could have done this with this problem right here and it would have taken this less time to just solve it but I want to find out the general pattern here so a plus B times a so we have a times a plus B that's this times this and then a plus B times negative B that's negative B times a plus B so I've done the distributive property once now I can do it again I can distribute the a onto the a and this B and it gives me a squared a times a is a squared plus a times B which is a B and now I can do it with the negative B negative B times a is negative a B or negative B a same thing and negative B times B is negative B squared now what does this simplify to well I have an a B and then I'm subtracting an a B so these two guys cancel out and I am just left with a squared minus B squared so the general pattern this is a good one to just kind of know a you know super fast is that a plus B times a minus B is always going to be a squared minus B squared so we have an a plus B times an a minus B so this product is going to be a squared so it's going to be 2x squared minus B squared minus a eight minus eight squared 2x squared that's the same thing as two squared times x squared or 4x squared and from that we're subtracting 8 squared so it's going to be 4x squared minus 64