Factoring 4(2x - 3y)^2 - 8(2x - 3y) - 21

[fdragon]

How did I do this problem?

4(2x-3y)²- 8(2x-3y)-21

From here I got it to....
16x²-36y²-16x+24y-21

The answer is (4x-6y+3)(4x-6y-7)............

I would like to know why you're suppose to use the factors from -36y² and -21 is there some kind of rule I don't know about? Something about the 2nd term and the last term or are you just suppose to guess and check until everything looks right?

 

[skeeter]

Re: Factoring 64a³+8

let u = (2x-3y)

now you have the expression 4u[sup:3aeyx9gz]2[/sup:3aeyx9gz] - 8u - 21

factor the above, then back substitute for u and simplify the factors.