Question

Answer 1

a: \(x^3\left(2x^3-\frac23x^2+\frac52\right)-\frac12x^5\)

\(=2x^6-\frac23x^5+\frac52x^3-\frac12x^5\)

\(=2x^6-\frac76x^5+\frac52x^3\)

b: \(x^2\left(2xy-y^2+2\right)=x^2\cdot2xy-x^2\cdot y^2+2x^2=2x^3y-x^2y^2+2x^2\)

c: \(x\left(x+xy\right)+2y\left(x^2-\frac{x^2}{y}\right)=x^2+x^2y+2x^2y-2x^2=-x^2+3x^2y\)

d: \(x^2\left(x^2-x+1\right)-2x\left(x-x^2\right)\)

\(=x^4-x^3+x^2-2x^2+2x^3=x^4+x^3-x^2\)