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\(a,\left(5x-2y\right)\left(x^2-xy+1\right)=5x^3-5x^2y+5x-2x^2y-2xy^2-2y=5x^3-7x^2y-2xy^2+5x-2y\)\(b\left(x-1\right)\left(x+1\right)\left(x-2\right)=\left(x^2-1\right)\left(x+2\right)=x^3+2x^2-x-2\)\(c,\dfrac{1}{2}x^2y^2\left(2x+y\right)\left(2x-y\right)=\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)=2x^4y^2-\dfrac{1}{2}x^2y^4\)
a: \(=xy^2+xy+x-y^3-y^2-y+\dfrac{2}{3}x^3y+\dfrac{1}{3}x^2y^3-2xy-y^3\)
\(=xy^2-xy+x-2y^3-y^2-y+\dfrac{2}{3}x^3y+\dfrac{1}{3}x^2y^3\)
b: \(=2x^3-4x^2+3x^3-3x^2-6x-15+5x^2\)
\(=5x^3-2x^2-6x-15\)
c: \(=x^2-4x+3+\left(x-4\right)\left(2x-1\right)-3x^3+2x-5\)
\(=-3x^3+x^2-2x-2+2x^2-x-8x+4\)
\(=-3x^3+3x^2-11x+2\)
a) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1\right)\left(2x+1\right)}{2x^2-1}-\dfrac{\left(2x-1\right)\left(2x-1\right)}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1\right)^2-\left(2x-1\right)^2}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1-2x-1\right)\left(2x+1+2x-1\right)}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\dfrac{4x}{2x^2-1}.\dfrac{5\left(2x-1\right)}{4x}\)
\(=\dfrac{5}{2x+1}\)
b) \(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1}{x^2+1}-\dfrac{x\left(2-x\right)}{x\left(x+1\right)}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{1}{x}+\dfrac{x^2}{x}-\dfrac{2x}{x}\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{x^2-2x+1}{x}\right)\)
\(=\dfrac{\left(x-1\right)^2}{x^2+1}.\dfrac{x}{\left(x-1\right)^2}\)
\(=\dfrac{x}{x^2+1}\)
c) d) Tự làm đi mình làm biếng quass >.< ^^
a: \(=2x^2-x+5\)
b: \(=-\dfrac{3}{2}x^3+x^2-\dfrac{1}{2}x\)
c: \(=-x^3+\dfrac{3}{2}-2x\)
d: \(=-2x^2+4xy-6y^2\)
e: \(=\dfrac{3}{5}\left(x-y\right)^3-\dfrac{2}{5}\left(x-y\right)^2+\dfrac{3}{5}\)
a) (x2 – 2x + 3) (1212x – 5)
= 1212x3 - 5x2 - x2 +10x + 3232x – 15
= 1212x3 – 6x2 + 232232x -15
b) (x2 – 2xy + y2)(x – y)
= x3 - x2 y - 2x2 y + 2xy2 +xy2- y3
= x3 - 3x2 y + 3xy2 - y3
a) (x2 – 2x + 3) ( 1/2x – 5) = \(\dfrac{1}{2}\)x3 – 5x2 – x2 + 10x +\(\dfrac{3}{2}\)x - 15
= \(\dfrac{1}{2}\)x3 – 6x2 + \(\dfrac{23}{2}\) x – 15.
b) (x2 – 2xy + y2)( x – y) = x3 – x2y – 2x2y + xy2 – y3 = x3 – 3x2y + 3xy2 – y3