Question

simpliy the following: (a) {[4x^2-49]/[8x^3+27]} *{ [4x^2+12x+9]/[2x^2-13x+21]} (b) {[x^2+x-6]/[x^2+7x-6]}*{[20x^2-7x-3]/[6x^2-25x+4]}*{[4x^2-11x-3]/[6x^2-19x+3]}

Answer 1

Here's (a):

{[4x^2-49]/[8x^3+27]} *{ [4x^2+12x+9]/[2x^2-13x+21]}

4x^2-49 = (2x-7)(2x+7)
8x^3+27 = (2x+3)(4x^2-6x+9)
4x^2+12x+9 = (2x+3)(2x+3)
2x^2-13x+21 = (2x-7)(x-3)

Putting it all together, you can cancel the (2x-7)(2x+3) to get

(2x+7)(2x+3) / (x-3)(4x^2-6x+9)

Do (b) likewise. The key is to know how to factor these babies. Recognize differences of square and cubes.

Answer 2

simpliy the expression by adding like terms and write the expression in descending powers of x 4x²+11x-3x²-12+x