Question

simplify:
8x^2(7-2x) / 3x(2x-7)

Answer 1

what we will do first is to distribute the top and the bottom.

For the top: you multiply 8x^2 to each of the two items. so we have 8x^2*7+8x^2*(-2x) which is 56x^2-16x^3 on top.

For the bottom: you multiply 3x to each of the two items. so we have 3x*2x + 3x*(-7) which is 6x^2 -21x.

So our answer so far is (56x^2-16x^3)/(6x^2-21x). Since each item has an x with it, we can factor it out of the top and the bottom and then cancel it from each.

Like so: [x(56x-16x^2)]/[x(6x-21)] = (56x-16x^2)/(6x-21).

we can factor the top from (56x-16x^2) to -8x(2x-7) and factor the bottom from (6x-21) to 3(2x-7). Since we have a (2x-7) on the top and bottom, we can cancel it from each. And then we are left with just -8x on the top and 3 on the bottom, making our answer: -8x/3 :)