Question

Factorise: (10) 9x² - 6x + 1 - 16y²​

Answer 1

Answer:

For a typical quadratic equation you have

aX2+bX+c

But, in this case you have something slightly different.

what you have is an equation such that you want to split it up into

(aX+bY)(cX+dY)

I’m ignoring the fact that this does come out to be a perfect square here, since YOU don’t know it.

Now, you have certain conditions for it, namely the coefficients;

a∗c=9

b∗d=16

a∗d+b∗c=24

Now, you’d normally need to fiddle around with those a bit — but notice that 9 and 16 are both Perfect Squares

32=9;42=16

Now, was this nice enough that the third equation works with 3 and 4? Well, a little math

3∗4=12;12+12=24

Yes! It does.

This means that

9x2+24xy+16y2=(3x+4y)2

Now, I have to assume that you typed in the question incorrectly - because there is not a ready and easy way to factor it if it is -16 rather than +16, at least not with the +24xy in the middle, because

(3x+4y)(3x−4y)=9x2−16y2

And you would still be left with the 24xy outside of the factored equation.

If you did type it up correctly, than Douglas Magowan has it right in that it’s Messy.