\(1)4x^2-25+\left(2x+7\right).\left(5.2x\right)\)

\(=\left(2x\right)^2-5^2-\left(2x+7\right).\left(2x-5\right)\)

\(=\left(2x.5\right)\left(2x+5\right).\left(2x+7\right)\left(2x-5\right)\)

\(=\left(2x-5\right)\left(2x+5-2x+7\right)\)

\(=\left(2x-5\right).12\)

\(2)3x+4-x^2-4x\)

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

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

\(3)5x^2-2y^2-10x+10y\)

\(=5\left(x^2-y^2\right)-10\left(x-4\right)\)

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

\(=\left(x-y\right)[5(x+y)-10]\)

Còn lại bn lm nốt nha! 

\(a,=2\left(\dfrac{1}{4}x^2-y^2\right)=2\left(\dfrac{1}{2}x-y\right)\left(\dfrac{1}{2}x+y\right)\\ b,=\dfrac{1}{3}x\left(y+3xz+3z\right)\\ c,=2x\left(9x^2-\dfrac{4}{25}\right)=2x\left(3x-\dfrac{2}{5}\right)\left(3x+\dfrac{2}{5}\right)\)

\(d,=x^2\left(\dfrac{2}{5}+5x+y\right)\\ e,=\dfrac{1}{2}\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\\ =\dfrac{1}{2}\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)^2\left(x+y\right)^2\\ f,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ g,=\dfrac{1}{2}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=\dfrac{1}{2}\left(x+\dfrac{1}{4}\right)^2\)

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)

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)

x²-y²-2x+2y

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

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

2)

2x+2y-x²-xy

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

=(2-x)(x+y)

3)

3a²-6ab+3b²-12c²

=3(a²-2ab+b²)-3(4c²)

=3(a-b)²-3(4c²)

=3[(a-b)²-4c² ]

=3(a-b-2c)(a-b+2c)

4)

x²-25+y²+2xy

=(x+y)²-25

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

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

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

4) x^2 - 25 + y^2 +2xy = x^2 + 2xy + y^2 - 25 = (x+y)^2 - 5^2 = (x+y-5)(x+y+5)

5) a^2 + 2ab +b^2-ac-bc= (a+b)^2- ac + bc = (a+b)^2 - c(a+b) = (a+b)(a+b-c)

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

7) x^2y - x^3 - 9y + 9x = x^2 (y-x) - 9(y-x) = (x^2 - 9)(y-x)= (x^2 - 3^2)(y-x) = (x-3)(x+3)(y-x)

- Xl câu 3 , 8 t hk biết lm

\(a,=\dfrac{1}{2}\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\\ =\dfrac{1}{2}\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)^2\left(x+y\right)^2\\ b,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ c,=\dfrac{1}{2}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=\dfrac{1}{2}\left(x+\dfrac{1}{4}\right)^2\)

a) 3x³ + 6x²y

= 3x².(x + 2y)

b) 2x³ - 6x²

= 2x².(x - 2)

c) 18x² - 20xy

= 2x.(9x - 10y)

d) xy + y² - x - y

= (xy + y²) - (x + y)

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

= (x + y)(y - 1)

e) (x²y² - 8)² - 1

= (x²y² - 8 - 1)(x²y² - 8 + 1)

= (x²y² - 9)(x²y² - 7)

= (xy - 3)(xy + 3)(x²y² - 7)

f) x² - 7x - 8

= x² - 8x + x - 8

= (x² - 8x) + (x - 8)

= x(x - 8) + (x - 8)

= (x - 8)(x + 1)

a: \(3x^3+6x^2y\)

\(=3x^2\cdot x+3x^2\cdot2y=3x^2\left(x+2y\right)\)

b: \(2x^3-6x^2=2x^2\cdot x-2x^2\cdot3=2x^2\left(x-3\right)\)

c: \(18x^2-20xy=2x\cdot9x-2x\cdot10y=2x\left(9x-10y\right)\)

d: \(xy+y^2-x-y\)

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

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

e: \(\left(x^2y^2-8\right)^2-1\)

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

\(=\left(x^2y^2-7\right)\left(x^2y^2-9\right)\)

\(=\left(x^2y^2-7\right)\left(xy-3\right)\left(xy+3\right)\)

f: \(x^2-7x-8\)

\(=x^2-8x+x-8\)

\(=x\left(x-8\right)+\left(x-8\right)=\left(x-8\right)\left(x+1\right)\)

g: \(10x^2\left(2x-y\right)+6xy\left(y-2x\right)\)

\(=2x\cdot\left(2x-y\right)\cdot5x-2x\cdot\left(2x-y\right)\cdot3y\)

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

h: \(x^2-2x+1-y^2\)

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

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

i: \(2x\left(x+2\right)+x^2\left(-x-2\right)\)

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

k: \(-x^2+6x-9=-\left(x^2-6x+9\right)\)

\(=-\left(x^2-2\cdot x\cdot3+3^2\right)=-\left(x-3\right)^2\)

l: \(-2x^2+8xy-8y^2\)

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

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

m: \(3x^2+5x-3y^2-5y\)

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

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

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

g) 10x²(2x - y) + 6xy(y - 2x)

= 10x²(2x - y) - 6xy(2x - y)

= 2x(2x - y)(5x - 3y)

h) x² - 2x + 1 - y²

= (x² - 2x + 1) - y²

= (x - 1)² - y²

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

i) 2x(x + 2) + x² (-x - 2)

= 2x(x + 2) - x²(x + 2)

= x(x + 2)(2 - x)

k) -9 + 6x - x²

= -(x² - 6x + 9)

= -(x - 3)²

l) 8xy - 2x² - 8y²

= -2(x² - 4xy + 4y²)

= -2(x - 2y)²

m) 3x² + 5x - 3y² - 5y

= (3x² - 3y²) + (5x - 5y)

= 3(x² - y²) + 5(x - y)

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

= (x - y)[3(x + y) + 5]

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

c: \(\left(x+y\right)^3-x^3-y^3\)

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

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

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