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\(\frac{3x^4-8x^3-10x^2+8x-5}{3x^2-2x+1}\)
\(=\frac{x^2\left(3x^2-2x+1\right)-2x\left(3x^2-2x+1\right)-5\left(3x^2-2x+1\right)}{3x^2-2x+1}\)
\(=\frac{\left(3x^2-2x+1\right)\cdot\left(x^2-2x-5\right)}{3x^2-2x+1}\)
\(=x^2-2x-5\)
\(\frac{2x^3-9x^2+19x-15}{x^2-3x+5}\)
\(=\frac{2x\left(x^2-3x+5\right)-3\left(x^2-3x+5\right)}{x^2-3x+5}\)
\(=\frac{\left(x^2-3x+5\right)\left(2x-3\right)}{x^2-3x+5}\)
\(=2x-3\)
a: \(\left(4x^5-8x^3\right):\left(-2x^3\right)\)
\(=-4x^5:2x^3+8x^3:2x^3\)
\(=-2x^2+4\)
b: \(\left(9x^3-12x^2+3x\right):\left(-3x\right)\)
\(=-\frac{9x^3}{3x}+\frac{12x^2}{3x}-\frac{3x}{3x}\)
\(=-3x^2+4x-1\)
c: \(\left(xy^2+4x^2y^3-3x^2y^4\right):\left(-\frac12x^2y^3\right)\)
\(=-xy^2:\frac12x^2y^3-4x^2y^3:\frac12x^2y^3+3x^2y^4:\frac12x^2y^3\)
\(=-\frac{2}{xy}-8+6y\)
d: \(\left\lbrack2\left(x-y\right)^3-7\left(y-x\right)^2-\left(y-x\right)\right\rbrack:\left(x-y\right)\)
\(=\left\lbrack2\left(x-y\right)^3-7\left(x-y\right)^2+\left(x-y\right)\right\rbrack:\left(x-y\right)\)
\(=\frac{2\left(x-y\right)^3}{x-y}-\frac{7\left(x-y\right)^2}{x-y}+\frac{\left(x-y\right)}{x-y}\)
\(=2\left(x-y\right)^2-7\left(x-y\right)+1\)
Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
a , x(3-x)-y(y-2x)+y(y-2)-x(2y-x)
=3x-x2-y2+2xy+y2-2y-2xy+x2
=3x-(-x2+x2)+(2xy-2xy)-2y
=3x-2y
b,(x2-7)(x+2)-(2x-1)(x-14)+x(x2-2x-22)+35
=x3+2x2-7x-14-2x2+29x-14+x3-2x2-22x+35
=(x3+x3)+(2x2-2x2-2x2)-(-7x+29x-22x)-14-14+35
=2x3-2x2+7
c,(2x+y)(4x2-2xy+y2)-8x3-y3
=2xy2-4x2y+8x3+y3-2xy2+4x2y-8x3-y3
=(2xy2-2xy2)-(-4x2y+4x2y)+(8x3-8x3)+(y3-y3)
=0
a) (𝑥−5)(𝑥+7)
𝑥(𝑥+7)−5(𝑥+7)
𝑥2+7𝑥−5(𝑥+7)
𝑥2+7𝑥−5𝑥−35
𝑥2+2𝑥−35
b) (𝑥−3)(𝑥2+5𝑦)
𝑥(𝑥2+5𝑦)−3(𝑥2+5𝑦)
𝑥3+5𝑥𝑦−3(𝑥2+5𝑦)
𝑥3+5𝑥𝑦−3𝑥2−15𝑦
𝑥3−3𝑥2+5𝑥𝑦−15𝑦