Question

 

Thực hiện phép tính 

2x².(3x-5x³)+10x⁵-5x³(x+2)(x²-2x+4)+(x-4)(x+2)

 

Answer 1

\(2x^2\left(3x-5x^3\right)+10x^5-5x^3\)

\(=\left(6x^3-10x^5\right)+10x^5-5x^3\)

\(=6x^3-10x^5+10x^5-5x^3\)

\(=\left(6x^3-5x^3\right)-\left(10^5-10^5\right)\)

\(=x^3\)

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

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

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

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

\(=\left(x+2\right)\left(-1+x\right)\)

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

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