Now we’re going to be looking at the perfect square. Now, what is a perfect square? It’s simply um an expression that looks like this a quadratic that looks like this x squared plus 2ax plus a squared. Now remember what we had in part one, we’ve had an
but with a perfect square, consider a case like this. Consider where a and b are equal. If they’re equal then it would be b, I’ll change that to a as well because they’re equal. And here, I’ll change b to a so it’s going to be times a, okay?
If they were equal then this would be what’s a plus a? It’s 2a and what’s a times a? a squared. So that’s when we have a perfect square when the two numbers two factors are equal. So we know that on our left again we draw our cross method, so we have on our left x times x to get x squared and on our right, we look at the factors of the last term which is a squared and we know that a times a makes a squared, okay? And then we cross multiply to check if we’ve got the middle one. So x times a is ax and x times a is also ax.
Now if you add them up we get 2ax because it’s the same thing we have two of each two of the same thing so we have 2ax which is the same as the middle one. So we do our usual thing so this is pretty much the same thing as what we’ve been doing in the last section. So x plus a times x plus a but see how this and this is exactly the same then we shouldn’t write it like this you can factor um you can go a little bit further we can make it x plus a squared because we have two of the same kind, okay and this is the factorization of this and we know that by this because we have a square it’s a perfect square when the factors are equal we call it a perfect square, okay? So that’s the idea. It’s pretty much the same idea.
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