1) \(3x\left(x-1\right)+5\left(x-1\right)\)

\(=\left(x-1\right)\left(3x+5\right)\)

2) \(4x(x-2y)-8y(2y-x)\)

\(=4x\left(x-2y\right)+8y\left(x-2y\right)\)

\(=\left(4x+8y\right)\left(x-2y\right)\)

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

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

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

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

\(=\left(a-b\right)\left(a+b\right)\left(x-1\right)\)

4) \(3x\left(x-a\right)+4a\left(a-x\right)\)

\(=3x\left(x-a\right)-4a\left(x-a\right)\)

\(=\left(x-a\right)\left(3x-4a\right)\)

5) \(5x\left(x-y\right)^2+10y^2\left(y-x\right)^2\)

\(=5x\left(x-y\right)^2+10y^2\left(x-y\right)^2\)

\(=\left(5x+10y^2\right)\left(x-y\right)^2\)

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

6) \(3x\left(x-3\right)^2+9\left(3-x\right)^2\)

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

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

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

7) \(x\left(m-a\right)^2-y\left(a-m\right)^2\)

\(=x\left(a-m\right)^2-y\left(a-m\right)^2\)

\(=\left(x-y\right)\left(a-m\right)^2\)

8) \(6y^2\left(x-1\right)^2+9y\left(1-x\right)^2\)

\(=6y^2\left(x-1\right)^2+9y\left(x-1\right)^2\)

\(=\left(6y^2+9x\right)\left(x-1\right)^2\)

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

#Ayumu

1, a ( a - b ) ( a + b )  - ( a + b ) ( a² - ab + b² )

= ( a + b ) [ a ( a - b ) - ( a² - ab + b² )

= ( a + b ) ( a² - ab - a² + ab - b² )

= ( a + b ) b²

.......

2, 3x ( x + 7 )² - 11x² ( x + 7 ) + 9 ( x + 7 )

= ( x + 7 ) [( 3x ( x + 7 ) - 11x² + 9 ]

= ( x + 7 ) ( 3x³ + 21x - 11x² + 9)

= ( x + 7 ) ( - 8x² + 21x + 9 )

..........

3, 4x ( x - 2y ) + 8y ( 2y - x )

= 4x ( x - 2y ) - 8y ( x - 2y )

=  ( 4x - 8y ) ( x - 2y )

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

= 4 ( x - 2y )²

1,a(a-b)(a+b)-(a+b)(a²-ab+b²)=(a+b)[a(a-b)-a²+ab-b²]

                                                =(a+b)(a²-ab-a²+ab-b²)

                                                =(a+b)(-b²)=-b²(a+b)

a) \(5x^2\)\(\left(x-2y\right)\)\(-\)\(15x\)\(\left(x-2y\right)\)

\(=\left(x-2y\right)\left(5x^2-15x\right)\)

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

b)  \(3\left(x-y\right)\)\(-\)\(5x\left(y-x\right)\)

\(=3\left(x-y\right)+5x\left(x-y\right)\)

\(=\left(x-y\right)\left(3+5x\right)\)

c)  \(10x\left(x-y\right)\)\(-\)\(8y\left(y-x\right)\)

\(=\)\(10x\left(x-y\right)+8y\left(x-y\right)\)

\(=\left(x-y\right)\left(10x+8y\right)\)

\(=2\left(5x+4\right)\left(x-y\right)\)

d)  \(x^2\)\(\left(x-5\right)\)\(+\)\(4\)\(\left(5-x\right)\)

\(=x^2\)\(\left(x-5\right)\)\(-\)\(4\left(x-5\right)\)

\(=\left(x-5\right)\left(x^2-4\right)\)

\(=\left(x-5\right)\left(x-2\right)\left(x-2\right)\)

a) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)

\(=\left(x-2y\right)\left(5x^2-15x\right)\)

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

b)\(3\left(x-y\right)-5x\left(y-x\right)\)

\(=3\left(x-y\right)+5x\left(x-y\right)\)

\(=\left(3+5x\right)\left(x-y\right)\)

c)\(10x\left(x-y\right)-8y\left(y-x\right)\)

\(=10x\left(x-y\right)+8y\left(x-y\right)\)

\(=\left(10x+8y\right)\left(x-y\right)\)

\(=2\left(5x+4y\right)\left(x-y\right)\)

d)\(x^2\left(x-5\right)+4\left(5-x\right)\)

\(=x^2\left(x-5\right)-4\left(x-5\right)\)

\(=\left(x^2-4\right)\left(x-5\right)\)

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

1D  2C

Câu 1: D

Câu 2: C

1. C. \(16x^2\left(x-y\right)\)\(-10y\left(y-1\right)\)\(=-2\left(y-x\right)\)\(\left(8x^2+5y\right)\)

2. C. \(\left(x-y\right)\left(x-y-3\right)\)

3. D. \(\left(x-2\right)\left(x+1\right)\)

4. C. \(y\left(x-2\right)\)\(5x\left(x-3\right)\)

5. D. \(3\left(x-2y\right)\)

1. Trong các kết quả sau kết quả nào sai

A. -17x^3y-34x^2y^2+51xy^3=17xy(x^2+2xy-3y^2)

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

C. 16x^2(x-y)-10y(y-1)=-2(y-x)(8x^2+5y)

2. Đa thức (x-y)^2+3(y-x) được phân tích thành nhân tử là:

A. (x+y)(x-y+3)

B. (x-y)(2x-2y+3)

C. (x-y)(x-y-3)

D. Cả 3 câu đều sai

3. Kết quả phân tích đa thức x(x-2)+(x-2) thành nhân tử

A. (x-2)x

B. (x-2)^2.x

C. x(2x-4)

D. (x-2)(x+1)

4. Kết quả phân tích 5x^2(xy-2y)-15x(xy-2y) thành nhân tử

A. (xy-2y)(5x^2-15x^2)

B. y(x-2)(5x^2-15x^2)

C. y(x-2)5x(x-3)

D. (xy-2y)5x(x-3)

5. Kết quả phân tích đa thức 3x-6y thành nhân tử là

A. 3(x-6y)

B. 3(3x-y)

C. 3(3x-2y)

D. 3(x-2y)

1. Trong các kết quả sau kết quả nào sai

A. -17x^3y-34x^2y^2+51xy^3=17xy(x^2+2xy-3y^2)

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

C. 16x^2(x-y)-10y(y-1)=-2(y-x)(8x^2+5y)

2. Đa thức (x-y)^2+3(y-x) được phân tích thành nhân tử là:

A. (x+y)(x-y+3)

B. (x-y)(2x-2y+3)

C. (x-y)(x-y-3)

D. Cả 3 câu đều sai

3. Kết quả phân tích đa thức x(x-2)+(x-2) thành nhân tử

A. (x-2)x

B. (x-2)^2.x

C. x(2x-4)

D. (x-2)(x+1)

4. Kết quả phân tích 5x^2(xy-2y)-15x(xy-2y) thành nhân tử

A. (xy-2y)(5x^2-15x^2)

B. y(x-2)(5x^2-15x^2)

C. y(x-2)5x(x-3)

D. (xy-2y)5x(x-3)

5. Kết quả phân tích đa thức 3x-6y thành nhân tử là

A. 3(x-6y)

B. 3(3x-y)

C. 3(3x-2y)

D. 3(x-2y)

2:

a: \(=\left(2x^2-xy\right)+\left(2xz-yz\right)\)

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

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

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

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

c: \(=\left(y^2+10y+25\right)-9z^2\)

\(=\left(y+5\right)^2-\left(3z\right)^2\)

\(=\left(y+5+3z\right)\left(y+5-3z\right)\)

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

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

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

1:

a: \(x\left(3-4x\right)+5\left(3-4x\right)=\left(3-4x\right)\left(x+5\right)\)

b: \(2y\left(5y-6\right)-4\left(6-5y\right)\)

\(=2y\left(5y-6\right)+4\left(5y-6\right)\)

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

c: \(=27\left(x-2\right)^3-3x\left(x-2\right)^2\)

\(=3\left(x-2\right)^2\cdot\left[9\left(x-2\right)-x\right]\)

\(=3\left(x-2\right)^2\left(8x-18\right)=6\left(x-2\right)^2\cdot\left(4x-9\right)\)

d: \(=6y\left(x-y\right)\left(x+y\right)-8y\left(x+y\right)^2\)

\(=2y\left(x+y\right)\left[3\left(x-y\right)-4\left(x+y\right)\right]\)

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

\(=2y\left(x+y\right)\left(-x-7y\right)\)

Bài 1

a) x(3 - 4x) + 5(3 - 4x)

= (3 - 4x)(x + 5)

b) 2y(5y - 6) - 4(6- 5y)

= 2y(5y - 6) + 4(5y - 6)

= (5y - 6)(2y + 4)

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

c) 27(x - 2)³ - 3x(2 - x)²

= 27(x - 2)³ - 3x(x - 2)²

= 3(x - 2)²[9(x - 2) - x]

= 3(x - 2)²(9x - 18 - x)

= 3(x - 2)²(8x - 18)

= 6(x - 2)²(4x - 9)

d) 6y(x² - y²) - 8y(x + y)²

= 6y(x - y)(x + y) - 8y(x + y)²

= 2y(x + y)[3(x - y) - 4(x + y)]

= 2y(x + y)(3x - 3y - 4x - 4y)

= 2y(x + y)(-x - 7y)

= -2y(x + y)(x + 7y)