Question

thực hiện phép chia :

[ 10x^2 (x+2)^3 -8x^3(x+2)^2+4x(x+2)^3] : 2x(x+2)^2

Answer 1

\(\dfrac{10x^2\left(x+2\right)^3-8x^3\left(x+2\right)^2+4x\left(x+2\right)^3}{2x\left(x+2\right)^2}\)

\(=\dfrac{10x^2\left(x+2\right)^3}{2x\left(x+2\right)^2}-\dfrac{8x^3\left(x+2\right)^2}{2x\left(x+2\right)^2}+\dfrac{4x\left(x+2\right)^3}{2x\left(x+2\right)^2}\)

\(=\dfrac{2x\cdot\left(x+2\right)^2\cdot5x\cdot\left(x+2\right)}{2x\left(x+2\right)^2}-\dfrac{2x\cdot\left(x+2\right)^2\cdot4x^2}{2x\left(x+2\right)^2}+\dfrac{2x\left(x+2\right)^2\cdot2\cdot\left(x+2\right)}{2x\left(x+2\right)^2}\)

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

\(=5x^2+10x-4x^2+2x+4\)

\(=x^2+12x+4\)