Bài giải:

a) (-2x⁵ + 3x² – 4x³) : 2x² = (- $\frac{2}{2}$)x^{5 – 2} + $\frac{3}{2}$x^{2 – 2} + (-$\frac{4}{2}$)x^{3 – 2} = - x³ + $\frac{3}{2}$ – 2x.

b) (x³ – 2x²y + 3xy²) : (- $\frac{1}{2}$x) = (x³ : -$\frac{1}{2}$x) + (-2x²y : -$\frac{1}{2}$x) + (3xy² : -$\frac{1}{2}$x)

= -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) \(\left(3x^2y^2+6x^2y^3-12xy\right):3xy\)

= \(\left(6x^2y^3:3xy\right)+\left(3x^2y^2:3xy\right)+\left(-12xy:3xy\right)\)

= \(xy^2+xy-4\)

sau bạn đăng tách ra cho mn cùng giúp nhé 

a, \(\left(-2x^5+3x^2-4x^3\right):2x^2=-x^3+\frac{3}{2}-2x\)

b, \(\left(x^3-2x^2y+3xy^2\right):\left(-\frac{1}{2}x\right)=-\frac{x^2}{2}+xy-\frac{3y^2}{2}\)

c, \(\left(3x^2y^2+6x^3y^3-12xy^2\right):3xy=xy+2x^2y^2-4y\)

d, \(\left(4x^3-3x^2y+5xy^2\right):\frac{1}{2}x=2x^2-\frac{3xy}{2}+\frac{5y^2}{2}\)

e, \(\left(18x^3y^5-9x^2y^2+6xy^2\right):3xy^2=6x^2y^3-3x+2\)

f, \(\left(x^4+2x^2y^2+y^4\right):\left(x^2+y^2\right)=\left(x^2+y^2\right)^2:\left(x^2+y^2\right)=x^2+y^2\)

trả lời hộ với mai thi rồi

đề bài là rút gọn à

a: \(N=\dfrac{3x^5-4x^4+6x^3}{-2x^2}=-\dfrac{3}{2}x^3+2x^2-3x\)

b: \(N=\dfrac{\left(6x^4y^5-3x^3y^4+\dfrac{1}{2}x^4y^3z\right)}{-\dfrac{1}{3}x^2y^3}=-18x^2y^2+9xy-\dfrac{3}{2}x^2z\)

c: \(\Leftrightarrow N\cdot\left(y-x\right)=\left(x-y\right)^3\)

\(\Leftrightarrow N=\dfrac{\left(x-y\right)^3}{y-x}=-\left(y-x\right)^2\)

d: \(\Leftrightarrow N\cdot\left(y^2-x^2\right)=\left(y^2-x^2\right)^2\)

hay \(N=y^2-x^2\)

\(a,3x\left(3x+6\right)=9x^2+18x\)

\(b,-\dfrac{1}{2}xy\left(4x^2+6x\right)\)

\(=-2x^3y-3x^2y\)

\(c,-2x^2y^3\left(\dfrac{1}{2}xy+4y^2\right)\)

\(=-x^3y^4-8x^2y^5\)

\(d,-6x^2\left(\dfrac{1}{3}xy^2-\dfrac{1}{2}y\right)\)

\(=-2x^3y^2+3x^2y\)

#\(Urushi\)

a) 3x(3x+6) = 9x^2 + 18x b) -1/2xy(4x^2+6x) = -2x^3y - 3xy c) -2x^2y^3(1/2xy+4y^2 ) = -x^2y^2 - 8x^2y^5 d) -6x^2(1/3xy^2-1/2y) = -2xy + 3x^2y

Vậy kết quả của các biểu thức là: a) 9x^2 + 18x b) -2x^3y - 3xy c) -x^2y^2 - 8x^2y^5 d) -2xy + 3x^2y