# Thread: Help simplifiying expression

1. ## Help simplifiying expression

Ok, so heres the problem, it asks me to simplify the expression:

{(2x-1)^4 * 3(x+3)^2 - 4(2x-1)^3 * 2(x+3)^3} / (2x-1)^8

I was thinking of using binomial therom since it looks like theres gonna be a lot of mulitplying

heres what i tried:

{(16x4+-32x3+24x2+-8x) * 3(1x2+6x1+9) - 4(8x3+-12x2+6x+-1) * 2(1x3+9x2+27x+27)} / (256x8+-1024x7+1792x6+-1792x5+1120x4+-448x3+112x2+-16x)

2. {(2x-1)^4 * 3(x+3)^2 - 4(2x-1)^3 * 2(x+3)^3} / (2x-1)^8

Easier if you start this way:
a = 2x - 1, b = x + 3 ; then:
(a^4 * 3b^2 - 4a^3 * 2b^3) / a^8

a^3(a * 3b^2 - 4 * 2b^3) / a^8 ... get my drift?
Then:
(a * 3b^2 - 4 * 2b^3) / a^5
(3ab^2 - 8b^3) / a^5
b^2(3a - 8b) / a^5

Now substitute back in.....

By the way, I see no reason why your teacher wouldn't be impressed if you submitted:

b^2(3a - 8b) / a^5 where a = 2x -1 and b = x + 3

Depends on the teacher, I guess....

3. thanks alot dude! i thought it'd be much harder from looking at the big scary fraction