a) \(2xy\left(x^2+xy-3y^2\right)\)
\(=2xy.x^2+2xy.xy+2xy.\left(-3y^2\right)\)
\(=2x^3y+2x^2y^2-6xy^3\)
b) \(\left(x+2\right)\left(3x^2-4x\right)\)
\(=x.3x^2+x.\left(-4x\right)+2.3x^2+2.\left(-4x\right)\)
\(=3x^3-4x^2+6x^2-8x\)
\(=3x^3+2x^2-8x\)
c) \(\left(x^3+3x^2-8x-20\right):\left(x+2\right)\)
\(=\left(x^3+2x^2+x^2+2x-10x-20\right):\left(x+2\right)\)
\(=\left[\left(x^3+2x^2\right)+\left(x^2+2x\right)-\left(10x+20\right)\right]:\left(x+2\right)\)
\(=\left[x^2\left(x+2\right)+x\left(x+2\right)-10\left(x+2\right)\right]:\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+x-10\right):\left(x+2\right)\)
\(=x^2+x-10\)
d) \(\left(4x^2-4x-4\right):\left(x+4\right)\)
\(=\left[4x\left(x+4\right)-20x-4\right]:\left(x+4\right)\)
\(=\left[4x\left(x+4\right)-20\left(x+4\right)+76\right]:\left(x+4\right)\)
\(=4x-20+\dfrac{76}{x+4}\)
e) \(\left(2x^3-3x^2+x-2\right):\left(x+5\right)\)
\(=\left[2x^2\left(x+5\right)-13x^2+x-2\right]:\left(x+5\right)\)
\(=\left[2x^2\left(x+5\right)-13x\left(x+5\right)+66x-2\right]:\left(x+5\right)\)
\(=\left[2x^2\left(x+5\right)-13x\left(x+5\right)+66\left(x+5\right)-332\right]:\left(x+5\right)\)
\(=2x^2-13x+66-\dfrac{332}{x+5}\)
