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a)\(\left(x-y\right)\left(x^3+x^2y+xy^2+y^3\right)=x^4+x^3y+x^2y^2+xy^3-x^3y-x^2y^2-xy^3-y^4=x^4-y^4\)
b) \(x\left(3x-18\right)-3\left(x-4\right)\left(x-2\right)+8=3x^2-18x-3x^2+18x-24+8=-16\)
a, `(8x^3-4x^2): 4x -(4x^2-5x) : 2x + (2x)^2`
`=4x (2x^2-x) : 4x - 2x(2x-5/2 ) :2x + 4x^2`
`=2x^2-x-2x+5/2+4x^2`
`=6x^2-3x+5/2`
b, `(3x^3-x^2y) :x^2 -(xy^2+x^2y) :xy + 2x(x+1)`
`=x^2 (3x-y) :x^2 -xy(y+x) + (2x^2+2x)`
`=3x-y-y-x+2x^2+2x`
`=2x^2+4x-2y`
a/ 5x2y (x2y– 4xy2 + 7xy)
`=5x^4y^2-20x^3y^3+35x^3y^2`
b/ 3xy2 (x2y3 + x 2y – xy2 )
`=3x^3y^5+3x^3y^3-3x^2y^4`
c/ 3x(12x2 + 4x – 5) + 2x(9x2 – 6x + 7)
`=36x^3+12x^2-15x+18x^3-18x^2+14x`
`=54x^3-6x^2-x`
d/ 5x(2x2 – 9x – 5) – 9x (x2 - 7x – 4)
`=10x^3-45x^2-25x-9x^3+63x^2+36x`
`=x^3+18x^2+11x`
\(a,=3x^3y^3-3x^2y^3+3x^2y^4+3xy^5\\ b,=\left(2x^3-6x^2+10x-3x^2+9x-15\right):\left(x^2-3x+5\right)\\ =\left[2x\left(x^2-3x+5\right)-3\left(x^2-3x+5\right)\right]:\left(x^2-3x+5\right)\\ =2x-3\\ c,=\left[x^2\left(x-3\right)+\left(x-3\right)\right]:\left(x-3\right)=x^2+1\)
\(b,=3xy\left(xy+2xy^2-4\right):3xy\\ =xy+2xy^2-4\\ c,=\left[\left(2x^3-x^2+x\right)+\left(6x^2-3x+3\right)\right]:\left(2x^2-x+1\right)\\ =\left[x\left(2x^2-x+1\right)+3\left(2x^2-x+1\right)\right]:\left(2x^2-x+1\right)\\ =\left[\left(x+3\right)\left(2x^2-x+1\right)\right]:\left(2x^2-x+1\right)\\ =x+3\)
\(A=2x+xy^2-x^2y-2y\)
\(=2\left(x-y\right)-xy\left(x-y\right)\)
\(=\left(x-y\right)\left(2-xy\right)\)
\(=\left(-\dfrac{1}{2}-\dfrac{-1}{3}\right)\left(2-\dfrac{-1}{2}\cdot\dfrac{-1}{3}\right)\)
\(=\left(\dfrac{1}{3}-\dfrac{1}{2}\right)\cdot\left(2-\dfrac{1}{6}\right)\)
\(=\dfrac{-1}{6}\cdot\dfrac{11}{6}=-\dfrac{11}{36}\)
