Author Topic: Algebraic Factorisation Homework Help (Read 597 times) Tweet Share

slinkybench · « **on:** February 13, 2018, 08:23:51 pm »

I'm generally very good at factorisation, but a couple questions have really confused me.

I'd appreciate it if you could take a look!

1. 12x^2 - 8xy - 15y^2
2. 20 - 9x - 20x^2
3. x(x-y)^2 - xz^2

RuiAce · « **Reply #1 on:** February 13, 2018, 08:29:13 pm »

1 and 2 are just the usual method for factorising quadratics (you may have used the cross method or anything else). They are $(2x-3y)(6x+5y)$ and $(5+4x)(4-5x)$. If you have trouble with these you should post your progress.
$\text{As for 3, first factor out the obvious }x.\\ \boxed{x(x-y)^2 - xz^2 = x\left[(x-y)^2 - z^2 \right]}$
$\text{Then, apply the difference of two squares factorisation }a^2-b^2 = (a-b)(a+b)\\ \text{where }a=x-y\text{ and }b=z$
$\text{This gives}\\ \boxed{x\left[(x-y)^2 - z^2\right] = x\left[ (x-y)-z\right]\left[(x-y)+z\right]}$
And then throw out the unnecessary brackets

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Author Topic: Algebraic Factorisation Homework Help (Read 597 times) Tweet Share

slinkybench

Algebraic Factorisation Homework Help

RuiAce

Re: Algebraic Factorisation Homework Help

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