a)(-2x2)(x2-2x+3)\(\dfrac{1}{2}\)=(-2x4+4x3-6x2)\(\dfrac{1}{2}\)=-x4+2x3-3x2 b)(\(\dfrac{2}{3}\)xy2)(x2y-xy+\(\dfrac{x}{2}\)+\(\dfrac{1}{4}\))=\(\dfrac{2}{3}\)x3y3-\(\dfrac{2}{3}\)x2y3+\(\dfrac{x^2y^2}{3}\)+\(\dfrac{1}{6}\)xy2 c)(-2x+1)(2x2-\(\dfrac{1}{3}\)x+2)=-4x3+\(\dfrac{2}{3}\)x2-4x+2x2-\(\dfrac{1}{3}\)x+2=-4x3+\(\dfrac{8}{3}\)x2-\(\dfrac{13}{3}\)x+2 d)(x+y2)(x2+\(\dfrac{1}{2}\)y+\(\dfrac{3}{2}\)xy)=x3+\(\dfrac{1}{2}\)xy+\(\dfrac{3}{2}\)x2y+x2y2+\(\dfrac{1}{2}\)y3+\(\dfrac{3}{2}\)xy3
a: Ta có: \(\left(-2x^2\right)\cdot\dfrac{1}{2}\cdot\left(x^2-2x+3\right)\)
\(=-x^2\left(x^2-2x+3\right)\)
\(=-x^4+2x^3-3x^2\)
b: Ta có: \(\left(\dfrac{2}{3}xy^2\right)\cdot\left(x^2y-xy+\dfrac{1}{2}x+\dfrac{1}{4}\right)\)
\(=\dfrac{2}{3}xy^2\cdot x^2y-\dfrac{2}{3}xy^2\cdot xy+\dfrac{2}{3}xy^2\cdot\dfrac{1}{2}x+\dfrac{2}{3}xy^2\cdot\dfrac{1}{4}\)
\(=\dfrac{2}{3}x^3y^3-\dfrac{2}{3}x^2y^3+\dfrac{1}{3}x^2y^2+\dfrac{1}{6}xy^2\)
c: Ta có: \(\left(-2x+1\right)\left(2x^2-\dfrac{1}{3}x+2\right)\)
\(=-4x^3+\dfrac{2}{3}x^2-4x+2x^2-\dfrac{1}{3}x+2\)
\(=-4x^3+\dfrac{8}{3}x^2-\dfrac{13}{3}x+2\)
