\(1,P=2x^2-2y^2-x^2+2xy-y^2+x^2+2xy+y^2-4y^2\\ P=2x^2-6y^2+4xy\\ 2,\\ a,=x\left(x-y\right)+3\left(x-y\right)=\left(x+3\right)\left(x-y\right)\\ b,=x\left(x^2-4x-y^2+4\right)\\ =x\left[\left(x-2\right)^2-y^2\right]=x\left(x-y-2\right)\left(x+y-2\right)\\ c,=\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]-3\\ =\left(x^2+5x+4\right)\left(x^2+5x+6\right)-3\\ =\left(x^2+5x+5-1\right)\left(x^2+5x+5+1\right)-3\\ =\left(x^2+5x+5\right)^2-1-3\\ =\left(x^2+5x+5\right)^2-4\\ =\left(x^2+5x+5+2\right)\left(x^2+5x+5-2\right)=\left(x^2+5x+7\right)\left(x^2+5x+3\right)\)
\(3,\\ \left(2x^4+x^3-5x^2-3x-3\right):\left(x^2-3\right)\\ =\left(2x^4-6x^2+x^3-3x+x^2-3\right):\left(x^2-3\right)\\ =\left(x^2-3\right)\left(2x^2+x+1\right):\left(x^2-3\right)=2x^2+x+1\)
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