a) P+Q = (6\(x^2-2x^2y+y^2+5\)) + (\(4x^2+2x^2y-2y^2-7\))
= 6\(x^2-2x^2y+y^2+5\) + \(4x^2+2x^2y-2y^2-7\)
= \((6x^2+4x^2)+[\left(-2x^2y\right)+2x^2y]+\left(y^2-2y^2\right)+\left(5-7\right)\)
= \((6+4)x^2+[\left(-2\right)+2]x^2y+\left(1-2\right)y^2+\left(-2\right)\)
= 10\(x^2+0+(-1y^2)+\left(-2\right)\)
= \(10x^2-y^2-2\)
b) P- Q = (6\(x^2-2x^2y+y^2+5\)) - (\(4x^2+2x^2y-2y^2-7\))
= 6\(x^2-2x^2y+y^2+5\) - \(4x^2-2x^2y+2y^2+7\)
= \([\)6\(x^2+\left(-4x^2\right)]\)\(+[\left(-2x^2y)+(-2x^2y\right)]+\left(y^2+2y^2\right)+\left(5+7\right)\)
= \([6+(-4)]x^2+[\left(-2\right)+\left(-2\right)]x^2y+\left(1+2\right)y^2+12\)
= 2\(x^2+\left(-4x^2y\right)+3y^2+12\)
= 2\(x^2-4x^2y+3y^2+12\)
