1. ## factorisation question

x2+6x-y2-8y-7

2. ## Re: factorisation question

Originally Posted by Aviator_13
x2+6x-y2-8y-7
$\noindent By inspection,$

$x^2 + 6x - y^2 - 8y - 7 = (x + y + 7)(x - y - 1).$

3. ## Re: factorisation question

What do you mean by inspection? I know the answer to the question lmao. I just don't know how to get it.

4. ## Re: factorisation question

"By inspection" means "by looking at it", basically. So if you were asked to solve $x^2 +4x+4=0$ then you'd probably know by inspection the answer is $x=2$ without actually factorising it.

$x^2+6x-y^2-8y-7$

Trying to complete the square actually works out perfectly here.

$= x^2+6x+9-(y^2+8y+16)$

$= (x+3)^2-(y+4)^2$

$= (x+3+y+4)(x+3-(y+4))$

$= (x+y+7)(x-y-1)$

5. ## Re: factorisation question

Ohhh I see...Thank you.

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