3 x y 2 – 6 x 2 y = 3 x y (   y   –   2 x )

a: \(3xy^2-3x^3-6xy+3x\)

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

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

=3x(y-1-x)(y-1+x)

b: \(3x^2+11x+6\)

\(=3x^2+9x+2x+6\)

=3x(x+3)+2(x+3)

=(x+3)(3x+2)

c: \(-x^3-4xy^2+4x^2y+16x\)

\(=x\left(-x^2-4y^2+4xy+16\right)\)

\(=x\left\lbrack4^2-\left(x^2-4xy+4y^2\right)\right\rbrack\)

\(=x\cdot\left\lbrack4^2-\left(x-2y\right)^2\right\rbrack\)

=x(4-x+2y)(4+x-2y)

d: \(xz-x^2-yz+2xy-y^2\)

\(=z\left(x-y\right)-\left(x^2-2xy+y^2\right)\)

=z(x-y)-\(\left(x-y^{}\right)^2\)

=(x-y)(z-x+y)

e: \(4x^2-y^2-6x+3y\)

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

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

x 3   –   6 x 2 y   +   12 x y 2   –   8 y 3   =   x 3   –   3 . x 2 . ( 2 y )   +   3 . x . ( 2 y ) 2   –   ( 2 y ) 3     =   ( x   –   2 y ) 3

đáp án cần chọn là: D

Bài 1 yêu cầu gì em?

Bài 2:

\(a,x\left(x-1\right)+5\left(x-1\right)=\left(x+5\right)\left(x-1\right)\\ b,3x\left(x+1\right)+3\left(x+1\right)=\left(3x+3\right)\left(x+1\right)=3\left(x+1\right)\left(x+1\right)=3\left(x+1\right)^2\\ c,x\left(x-3\right)+xy\left(x-3\right)=\left(x+xy\right)\left(x-3\right)=x\left(y+1\right)\left(x-3\right)\\ d,2x\left(x-2\right)-6\left(x-2\right)=\left(2x-6\right)\left(x-2\right)=2\left(x-3\right)\left(x-2\right)\)

Bài 1:

a) \(3xy+6y\)

\(=3y\left(x+2\right)\)

b) \(3x^2+9x\)

\(=3x\left(x+3\right)\)

c) \(6x-9y^2\)

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

d) \(10xy^2-6x^2y\)

\(=2xy\left(5y-3x\right)\)

Bài 2:

a) \(x\left(x-1\right)+5\left(x-1\right)\)

\(=\left(x-1\right)\left(x+5\right)\)

b) \(3x\left(x+1\right)+3\left(x+1\right)\)

\(=\left(x+1\right)\left(3x+3\right)\)

\(=3\left(x+1\right)\left(x+1\right)\)

\(=3\left(x+1\right)^2\) 

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

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

\(=x\left(1+y\right)\left(x-3\right)\)

d) \(2x\left(x-2\right)-6\left(x-2\right)\)

\(=\left(2x-6\right)\left(x-2\right)\)

\(=2\left(x-3\right)\left(x-2\right)\)

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

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

\(a,=-\left(x-1\right)^3\left[=\left(1-x\right)^3\right]\\ b,=\left(1-x\right)^3\)

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

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

\(=\left(x+y\right)^3-\left(x+y\right)\)

\(=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)

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

=(x-y)(x^2-2xy+y^2-x-y)

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

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

\(=\left(x-y\right)^3-\left(x-y\right)\left(x+y\right)\)

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

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

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

\(x^3-6x^2y+12xy^2-8y^3=\left(x-2\right)^3\)