\(a)P\left(x\right)+Q\left(x\right)=4x^2y-2xy^2+x^2y-15+2xy+\left(2xy^2+3x^2y-4xy-x^2y^2\right)\)
\(=4x^2y^2-2xy^2+x^2y-15+2xy+2xy^2+3x^2y-4xy-x^2y^2\)
\(=\left(4x^2y^2-x^2y^2\right)+\left(-2xy^2+2xy^2\right)+\left(x^2y+3x^2y\right)-15+\left(2xy-4xy\right)\)
\(=3x^2y^2+4x^2y-2xy-15\)
\(P\left(x\right)-Q\left(x\right)=4x^2y^2-2xy^2+x^2y-15+2xy-\left(2xy^2+3x^2y-4xy-x^2y^2\right)\)
\(=4x^2y^2-2xy^2+x^2y-15+2xy-2xy^2-3x^2y+4xy+x^2y^2\)
\(=\left(4x^2y+x^2y^2\right)+\left(-2xy^2-2xy^2\right)+\left(x^2y-3x^2y\right)-15+\left(2xy+4xy\right)\)
\(=5x^2y-4xy^2-2x^2y+6xy-15\)
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