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Bài giải:
a) (-2x5 + 3x2 – 4x3) : 2x2 = (- 2222)x5 – 2 + 3232x2 – 2 + (-4242)x3 – 2 = - x3 + 3232 – 2x.
b) (x3 – 2x2y + 3xy2) : (- 1212x) = (x3 : -1212x) + (-2x2y : -1212x) + (3xy2 : -1212x)
= -2x2 + 4xy – 6y2
c)(3x2y2 + 6x2y3 – 12xy) : 3xy = (3x2y2 : 3xy) + (6x2y2 : 3xy) + (-12xy : 3xy)
= xy + 2xy2 – 4.
a) (-2x5+3x2-4x3) : 2x2
= (-2x5:2x2)-(4x3:2x2)+(3x2:2x2)
= -x3-2x+\(\dfrac{3}{2}\)
b) \(\left(x^3-2x^2y+3xy^2\right):\left(-\dfrac{1}{2}x\right)\)
= \(\left(x^3:\dfrac{-1}{2}x\right)+\left(-2x^2y:\dfrac{-1}{2}x\right)+\left(3xy^2:\dfrac{-1}{2}x\right)\)
= \(-2x^2+4xy-6y^2\)
c) \(\left(3x^2y^2+6x^2y^3-12xy\right):3xy\)
= \(\left(6x^2y^3:3xy\right)+\left(3x^2y^2:3xy\right)+\left(-12xy:3xy\right)\)
= \(xy^2+xy-4\)
a) \((2x^2−3x)(5x^2−2x+1)\)
\(=2x^2.5x^2−2x^2.2x+2x^2−3x.5x^2+3x.2x−3x\)
\(=10x^4−4x^3+2x^2−15x^3+6x^2−3x\)
\(=10x^4−19x^3+8x^2−3x\)
b) \((x−2y)(3xy+5y^2+x)\)
\(=x.3xy+x.5y^2+x.x−2y.3xy−2y.5y^2−2y.x\)
\(=3x^2y+5xy^2+x^2−6xy^2−10y^3−2xy\)
\(=3x^2y−xy^2−2xy+x^2−10y^3\)
a)\(\left(2x+1\right).\left(x-1\right)=2x^2-x-1\)
b) \(\frac{3xy+6x^2y-9xy}{3xy}=\frac{3xy+2x.\left(3xy\right)-3.\left(3xy\right)}{3xy}=\frac{\left(3xy\right).\left(1+2x-3\right)}{3xy}=2x-2=2.\left(x-1\right)\)