Question

(8x^3(2x-5)^2-6x^2(2x-5)^3+10x(2x-5)^2):2x(2x-5)^2

Answer 1

\(\dfrac{\left[8x^3\left(2x-5\right)^2-6x^2\left(2x-5\right)^3+10x\left(2x-5\right)^2\right]}{2x\left(2x-5\right)^2}\)

\(=\dfrac{8x^3\left(2x-5\right)^2}{2x\left(2x-5\right)^2}-\dfrac{6x^2\left(2x-5\right)^3}{2x\left(2x-5\right)^2}+\dfrac{10x\left(2x-5\right)^2}{2x\left(2x-5\right)^2}\)

\(=4x^2-3x\left(2x-5\right)+5\)

\(=4x^2-6x^2+15x+5=-2x^2+15x+5\)