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Үндсэн товъёог

# Identifying perfect square form

## Video transcript

we want to figure out what a X plus B squared is and I encourage you to pause the video and figure out what that is in terms of capital A and capital B so let's work through it this is the same thing as multiplying ax plus b times ax plus B so let me fill that in this is ax there another ax there I just wrote it in that order to make the color switching a little bit easier so ax plus B times ax plus B well what's that going to be equal to well if you take this ax and you multiply it times that ax you're going to get ax squared ax the entire thing squared and then if you take if you take this ax and then multiply it times this B you're going to get a b x then if you take this b and you multiply it times this ax you're going to get another a bx a b x and then last but not least if you take this B and multiply it times the other B it's going to be plus B squared and so what are you left with well you're going to be left with a I'll write it like this a x squared which we actually if we want well I'll write it in a different way in a second and then you have plus plus 2 it's a slightly different color let me do that other color plus 2 a B X and then finally plus B squared plus B squared now I said I could write it in a slightly different way what I could do is just rewrite out a x squared as being the same thing this is the same thing as a squared x squared and then I can write out everything else the same way plus 2 a B X and then plus B squared now why did I what's interesting about doing this well now we can see the pattern for the square of any binomial or binomial like this so for example if someone were to walk up to you and say alright I have I have a trinomial of the form let's say they have a trinomial of the form 25 x squared plus 20x plus 4 and they were to tell you to factor this well actually let's just do that why don't you pause the video and see if you could factor this is the product of two binomials well when you look at this you see what look you know this 25 x squared that looks like a square a perfect square 25 x squared that's the same thing as 5 squared x squared or you could write it as 5 x 5 x squared this 4 here that's a perfect square that's the same thing as 2 squared and let's see 20 right over here if if we wanted to fit this pattern we would say that a is 5 and B is 2 and so let's see what would be 2 times a B well 5 times 2 a B would be 10 and then 2 times that would be 20 so this right over here is that is plus 2 times 5 2 times 5 times 2 times 2 x times 2x other than this color times 2 X so you see that this completely matches this pattern here where a is equal to 5 and B is equal to 2 once again this is ax whole thing squared then you have 2 times a times B X we see that there and then finally you have the B squared so if you wanted to factor this you could say well this is just going to be the same thing since we know what a and B are this is going to be 5x + 2 5 X + 2 5 X plus 2 whole thing squared so the whole point of doing this is to start recognising when we actually have perfect squares especially perfect squares where the leading coefficient isn't one