Bài 2
a, \(-2x^3y\left(2x^2-3y+5xy\right)=-4x^5y+6x^3y-10x^4y^2\)
b, \(-2y\left(x^2y^2-xy+2y\right)=-2x^2y^3+2xy^2-4y^2\)
c, \(\dfrac{2}{5}x^2y\left(x^2y-5x+10y\right)=\dfrac{2}{5}x^4y^2-2x^3y+4x^2y^2\)
d, \(-\dfrac{1}{3}xy\left(\dfrac{3}{2}x^2y-xy+\dfrac{6}{5}x\right)=-\dfrac{1}{2}x^3y^2+\dfrac{1}{3}x^2y^2-\dfrac{2}{5}x^2y\)
Bài 1:
a: \(P+Q\)
\(=x^2y-x^3-xy^2+3+x^3+xy^2-xy-6\)
\(=x^2y-xy-3\)
P-Q
\(=x^2y-x^3-xy^2+3-x^3-xy^2+xy+6\)
\(=x^2y-2xy^2-2x^3+xy+9\)
b: M+N
\(=x^2y+xy^3-5x^3y^2+4x^3+3xy^3-x^2y+5x^3y^2\)
\(=4xy^3+4x^3\)
M-N
\(=x^2y+xy^3-5x^3y^2+4x^3-3xy^3+x^2y-5x^3y^2\)
\(=-10x^3y^2+2x^2y-2xy^3+4x^3\)
c: P+Q
\(=5x^2y+2x^3-xy^2+10+2x^3+5xy^2-xy-10\)
\(=5x^2y+4x^3+4xy^2-xy\)
P-Q
\(=5x^2y+2x^3-xy^2+10-2x^3-5xy^2+xy+10\)
\(=5x^2y-6xy^2+xy+20\)
d: M+N
\(=4x^2y-xy^3-3x^3y^2+x^3+3xy^3-4x^2y+3x^3y^2\)
\(=2xy^3+x^3\)
M-N
\(=4x^2y-xy^3-3x^3y^2+x^3-3xy^3+4x^2y-3x^3y^2=8x^2y-4xy^3-6x^3y^2+x^3\)
Bài 3
a, \(\left(x-y\right)\left(x^2+xy+y^2\right)=x^3+x^2y+xy^2-x^2y-xy^2-y^3=x^3-y^3\)
b, \(\left(\dfrac{1}{2}xy-1\right)\left(x^3-2x-6\right)=\dfrac{x^4y}{2}-x^2y-3xy-x^3+2x+6\)
c, \(\left(x-2y^2\right)\left(x^2+2xy+4y^4\right)=x^3+2x^2y+4xy^4-2x^2y^2-4xy^3-8y^6\)
d, \(\left(x-1\right)\left(x-2\right)x=\left(x^2-3x+2\right)x=x^3-3x^2+2x\)
