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

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

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

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

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

Vậy chọn đáp án A

chọn A

Bài 2: 

a: \(3x^2-3xy=3x\left(x-y\right)\)

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

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

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

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1 a

2c

3b

4d

5c

6c

Chon D

D

Phân tích đa thức thành nhân tử:

a) 5x - 5y

= 5(x - y)

b) 3xy² + x²y

= xy(3y + x)

c) 12x²y - 18xy² - 30y³

= 2y(6x² - 9xy - 15y²)

= 2y(6x² + 6xy - 15xy - 15y²)

= 2y[6x(x + y) - 15y(x + y)]

= 2y(x + y)(6x - 15y)

= 6y(x + y)(2x - 5y)

d) -17x³y - 34x²y² + 51xy³

= -17xy(x² + 2xy - 3y²)

= -17xy(x² - xy + 3xy - 3y²)

= -17xy[x(x - y) + 3y(x - y)]

= -17xy(x - y)(x + 3y)

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

= (y - 1)(x + 3)

f) 16²(x - y) - 10y(y - x)

= 16²(x - y) + 10y(x - y)

= (x - y)(16² + 10y)

= (x - y)(256 + 10y)

a) Ta có: 5x-5y

=5(x-y)

b) Ta có: \(3xy^2+x^2y\)

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

c) Ta có: \(12x^2y-18xy^2-30y^3\)

\(=6y\left(2x^2-3xy-5y^2\right)\)

\(=6y\left(2x^2-5xy+2xy-5y^2\right)\)

\(=6y\left[2x\left(x+y\right)-5y\left(x+y\right)\right]\)

\(=6y\left(x+y\right)\left(2x-5y\right)\)

d) Ta có: \(-17x^3y-34x^2y^2+51xy^3\)

\(=-17xy\left(x^2+2xy-3y^2\right)\)

\(=-17xy\left(x^2+3xy-xy-3y^2\right)\)

\(=-17xy\left[x\left(x+3y\right)-y\left(x+3y\right)\right]\)

\(=-17xy\left(x+3y\right)\left(x-y\right)\)

e) Ta có: x(y-1)+3(y-1)

=(y-1)(x+3)

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

2) \(y\left(x-2y\right)^2+xy^2\left(2y-x\right)=\left(2y-x\right)\left(2\left(2y-x\right)+1\right)=\left(2y-x\right)\left(4y-2x+1\right)\)

3) \(xy\left(x+y\right)-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\) (xem lại đề sửa -2x thành -x mới đúng)

4) \(xy\left(x-3y\right)-2x+6y=xy\left(x-3y\right)-2\left(x-3y\right)=\left(x-3y\right)\left(xy-2\right)\)

dài quá mình làm 3 câu đầu thôi nhé!

a)7x^2-14xy

=7x(x-2y)

b) 3x^2-6xy+3y^2

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

c) x^2-4z^2-2xy+y^2

=(x^2-2xy+y^2)-4z^2

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

=3(x-y)^2

c) 

a: =(6x)^2-(3x-2)^2

=(6x-3x+2)(6x+3x-2)

=(9x-2)(3x+2)

d: \(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)

\(=4x\cdot\left[x^2+2x+1+x^2-2x+1\right]\)

=8x(x^2+1)

e: =(4x)^2-2*4x*3y+(3y)^2

=(4x-3y)^2

f: \(=-\left(\dfrac{1}{4}x^4-2\cdot\dfrac{1}{2}x^2\cdot2y^3+4y^6\right)\)

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

g: =(4x)^3+1^3

=(4x+1)(16x^2-4x+1)

k: =x^3(27x^3-8)

=x^3(3x-2)(9x^2+6x+4)

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

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