Bài 9:
a) Thu gọn các đa thức M và N
\(M=3,5x^2y-2xy^2+1,5x^2y+2xy+3xy^2\)
\(=\left(3,5x^2y+1,5x^2y\right)+\left(-2xy^2+3xy^2\right)+2xy\)
\(=5x^2y+xy^2+2xy\)
\(N=2x^2y+3,2xy+xy^2-4xy^2-1,2xy\)
\(=2x^2y+\left(xy^2-4xy^2\right)+\left(3,2xy-1,2xy\right)\)
\(=2x^2y-3xy^2+2xy\)
b) \(M-N=\left(5x^2y+xy^2+2xy\right)-\left(2x^2y-3xy^2+2xy\right)\)
\(=5x^2y+xy^2+2xy-2x^2y+3xy^2-2xy\)
\(=\left(5x^2y-2x^2y\right)+\left(xy^2+3xy^2\right)+\left(2xy-2xy\right)\)
\(=3x^2y+4xy^2\)
Bài 10:
\(P\left(x\right)+Q\left(x\right)=\left(3x^2+x-4\right)+\left(-5x^2+x+3\right)\)
\(=3x^2+x-4-5x^2+x+3\)
\(=\left(3x^2-5x^2\right)+\left(x+x\right)+\left(-4+3\right)\)
\(=-2x^2+2x-1\)
\(P\left(x\right)-Q\left(x\right)=\left(3x^2+x-4\right)-\left(-5x^2+x+3\right)\)
\(=3x^2+x-4+5x^2-x-3\)
\(=\left(3x^2+5x^2\right)+\left(x-x\right)+\left(-4-3\right)\)
\(=8x^2-7\)
