\(2x^3y-2xy^3-4xy^2-2xy\)

\(=2xy.\left(x^2-y^2-2y-1\right)\)

\(=2xy.[x^2-\left(y^2+2y+1\right)]\)

\(=2xy.[x^2-\left(y+1\right)^2]\)

\(=2xy.\left(x+y+1\right).\left(x-y-1\right)\)

Vậy chọn đáp án A

chọn A

đề bài là rút gọn à

a) (x²-6xy+9y²):(3y-x)

= (x-3y)²:(3y-x)

=(3y-x)²:(3y-x)

= 3y-x

b) (8x³-1):(4x²+2x+1)

=[(2x)³-1]:(4x²+2x+1)

= (2x-1)(4x²+2x+1):(4x²+2x+1)

= 2x-1

c) (4x⁴-9):(2x²-3)

=(2x²-3)(2x²+3):(2x²-3)

=2x²+3

d) (8x³-27):(4x²+6x+9)

=(2x-3)(4x²+6x+9):(4x²+6x+9)

=2x-3

a) \(3xy-6xy^2=3xy\left(1-2y\right)\)

b) \(3x^3+6x^2+3x=3x\left(x^2+2x+1\right)=3x\left(x+1\right)^2\)

c) \(x^3-x^2+2\)

d) \(x^2+4x+4-y^2=\left(x^2+4x+4\right)-y^2=\left(x+2\right)^2-y^2=\left(x-y+2\right)\left(x+y+2\right)\)

e) \(x^3+4x^2+4x=x\left(x^2+4x+4\right)=x\left(x+2\right)^2\)

f) \(x^2+2x+1-9y^2=\left(x+1\right)^2-\left(3y\right)^2=\left(x-3y+1\right)\left(x+3y+1\right)\)

g) \(6x^2-12x=6x\left(x-2\right)\)

h) \(x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\)

i) \(x^2-2xy+y^2-9=\left(x-y\right)^2-3^2=\left(x-y-3\right)\left(x-y+3\right)\)

k) \(2x^3+2x^2y-4xy^2=2x\left(x^2+xy-2y^2\right)\)

l) \(x^3-7x^2+9x+3x^2-21x+27=x\left(x^2-7x+9\right)+3\left(x^2-7x+9\right)=\left(x+3\right)\left(x^2-7x+9\right)\)

\(c,\frac{2x+2}{x^2+4x+3}=\frac{2\left(x+1\right)}{x^2+3x+x+3}=\frac{2\left(x+1\right)}{x\left(x+3\right)+\left(x+3\right)}.\)

\(=\frac{2\left(x+1\right)}{\left(x+1\right)\left(x+3\right)}=\frac{2}{x+3}\)