Factorising Difference of Squares: Non-Monic Coefficients

Factorising Difference of Squares Non-Monic Coefficients
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All right! We’ve got x squared. But, what about 4? Try to change this whole thing to a square number guys. What squared is 4? 4 is two squared, isn’t it? And 9, 9 is 3 squared, so I can make this one, 2x, the whole thing squared because it’s 2 squared, x squared. So I can change this to 2x, the whole thing squared and this one is 3 squared, so this time we have 2x and 3, so we go 2x plus 3, 2x minus 3, okay? Get the idea?

So, that’s what we do. The same kind of thing, what squared is 16? 4, 4 squared is 16. And 25 is 5 squared.
So, this one guys, this one will be 4 squared and x squared, isn’t it? Which is 4x the whole thing squared? So you make it into 1 and 25 is 5 squared, so it’s going to be 4x and 5 that we’re going to be using, so it’s 4x plus 5, 4x minus 5, okay? So, it’s very very easy as long as you can identify the squares. Just be careful when you find the squares.

A fraction, but it’s okay. We do the same kind of thing. All right! This one, think about it like this guys. 4x squared over 9. It’s 4 over 9x squared, isn’t it? So 4 over 9, what squared is that? 4 over 9, it’s 4 is 2 squared, 9, it’s 3 squared and we’ve got the x squared. See how they’re all squares, so you can make that into 1 by changing it to 2x over 3, the whole thing squared, okay?

So you just need one bracket with one square and you know that 25 is 5 squared and 16 is 4 squared, so we just have 5 on 4 squared, just make it square minus a square like that. So this is what we concentrate and this is what we concentrate on, so it’s 2x oh sorry 2x over 3 plus 5 on 4 times 2x over 3 minus 5 over 4, okay? So it’s a bit more confusing when you have fractions but just keep it the same method. Trying to look at the squares of both numerator and denominator.


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