\(P=3x^2y+4y^2+5x^2y-x^3-6\)
\(=8x^2y+4y^2-x^3-6\)
\(Q=2x^3-3x^3y^4-x^2y+xy+4\)
a) \(P+Q=\left(8x^2y+4y^2-x^3-6\right)+\left(2x^3-3x^3y^4-x^2y+xy+4\right)\)
\(=8x^2y+4y^2-x^3-6+2x^3-3x^3y^4-x^2y+xy+4\)
\(=\left(8x^2y-x^2y\right)+4y^2+\left(-x^3+2x^3\right)-3x^3y^4+xy+\left(-6+4\right)\)
\(=7x^2y+4y^2+x^3-3x^3y^4+xy-2\)
\(P-Q=\left(8x^2y+4y^2-x^3-6\right)-\left(2x^3-3x^3y^4-x^2y+xy+4\right)\)
\(=8x^2y+4y^2-x^3-6-2x^3+3x^3y^4+x^2y-xy-4\)
\(=\left(8x^2y+x^2y\right)+4y^2+\left(-x^3-2x^3\right)+3x^3y^4-xy+\left(-6-4\right)\)
\(=9x^2y+4y^2-3x^3+3x^3y^4-xy-10\)
b) \(A=3Q-2P\)
\(=3\left(2x^3-3x^3y^4-x^2y+xy+4\right)-2\left(8x^2y+4y^2-x^3-6\right)\)
\(=6x^3-9x^3y^4-3x^2y+3xy+12-16x^2y-8y^2+2x^3+12\)
\(=\left(6x^3+2x^3\right)-8y^2-9x^3y^4+\left(-3x^2y-16x^2y\right)+3xy+\left(12+12\right)\)
\(=8x^3-8y^2-9x^3y^4-19x^2y+3xy+24\)
$\text{#}Toru$
