a) \(\left(\dfrac{3}{5}a^6x^3+\dfrac{3}{7}a^3x^4-\dfrac{9}{10}ax^5\right):\dfrac{3}{5}ax^3\)

\(=\dfrac{\dfrac{3}{5}a^6x^3+\dfrac{3}{7}a^3x^4-\dfrac{9}{10}ax^5}{\dfrac{3}{5}ax^3}\)

\(=\dfrac{\dfrac{3}{5}ax^3\left(a^5+\dfrac{5}{7}a^2x-\dfrac{3}{2}x^2\right)}{\dfrac{3}{5}ax^3}\)

\(=a^5+\dfrac{5}{7}a^2x-\dfrac{3}{2}x^2\)

b) \(\left(9x^2y^3-15x^4y^4\right):3x^2y-\left(2-3x^2y\right)\cdot y^2\)

\(=\dfrac{3x^2y\left(3y^2-5x^2y^3\right)}{3x^2y}-2y^2+3x^2y^3\)

\(=3y^2-5x^2y^3-2y^2+3x^2y^3\)

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

c) \(\left(6x^2-xy\right):x+\left(2x^3y+3xy^2\right):xy-\left(2x-1\right)x\)

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

\(=\dfrac{x\left(6x-y\right)}{x}+\dfrac{xy\left(2x^2+3y\right)}{xy}-2x^2+x\)

\(=6x-y+2x^2+3y-2x^2+x\)

\(=7x+2y\)

d) \(\left(x^2-xy\right):x+\left(6x^2y^5-9x^3y^4+15x^4y^2\right):\dfrac{3}{2}x^2y^3\)

\(=\dfrac{x^2-xy}{x}+\dfrac{6x^2y^5-9x^3y^4+15x^4y^2}{\dfrac{3}{2}x^2y^3}\)

\(=\dfrac{x\left(x-y\right)}{x}+\dfrac{\dfrac{3}{2}x^2y^2\left(4y^3-6xy^2+10x^2\right)}{\dfrac{3}{2}x^2y^3}\)

\(=x-y+\dfrac{4y^3-6xy^2+10x^2}{y}\)

20x4y - 25x2y2 - 3x2y = 5x2y . (4x2 - 5y - 3/5)

Nên (20x4y - 25x2y2 - 3x2y) : 5x2y = 4x2 - 5y - 3/5

\(=-2x^3y^2-2x^2y^2+\dfrac{2}{3}xy^3\)

Ta có

A + B = 3 x 3 y 2 + 2 x 2 y − x y + 4 x y − 3 x 2 y + 2 x 3 y 2 + y 2 = 3 x 3 y 2 + 2 x 3 y 2 + 2 x 2 y − 3 x 2 y + ( − x y + 4 x y ) + y 2 = 5 x 3 y 2 − x 2 y + 3 x y + y 2

Chọn đáp án D

-(x²+3xy²+3x²y+y²)

=-(x+y)³

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

\(\left(1-3y\right)x^2-3y^2x-y^2\)

\(\left(x+y\right)\left(-3xy+x-y\right)\)

= (x-y)(x+y) -3xy(x+y)
= (x-y)(x+y-3xy)

a, \(15^4-12x^3+9x^2\)

b,\(-15x^3y^2+25x^2y^2-5xy^3\)

c, \(5x^3-19x^2+12x\)

d, 

x3+xy2+5x2y−9x2y−3y3−15xy2=3x3−3y3−14xy2−4x2y

\(a,=15x^4-12x^3+9x^2\\ b,=-15x^3y^2+25x^2y^2-5xy^3\\ c,=5x^3-15x^2-4x^2+12x=5x^3-19x^2+12x\\ d,=3x^3+xy^2+5x^2y-9x^2y-3y^3-15xy^2=3x^3-14xy^2-4x^2y-3y^3\)