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

2, \(x^2-25+y^2+2xy=\left(x+y\right)^2-5^2=\left(x+y-5\right)\left(x+y+5\right)\)

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

4, \(x^4+2x^3+x^2=x^2\left(x^2+2x+1\right)=x^2\left(x+1\right)^2\)

5, \(x^4+8x=x\left(x^3+8\right)=x\left(x+8\right)\left(x^2-8x+64\right)\)

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)

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

tách nhỏ câu hỏi ra bạn

\(a.10x\left(x-y\right)-6y\left(y-x\right)\\ =10x\left(x-y\right)+6y\left(x-y\right)\\ =\left(10x-6y\right)\left(x-y\right)\\ =2\left(5x-3y\right)\left(x-y\right)\)

\(b.14x^2y-21xy^2+28x^3y^2\\ =7xy\left(x-y+xy\right)\)

\(c.x^2-4+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\\ =\left(x-2\right)\left(x+2+x-2\right)\\ =2x\left(x-2\right)\)

\(d.\left(x+1\right)^2-25\\ =\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)

a) \(2x^2-2y^2\)

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

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

b) \(x^2-4x+4\)

\(=x^2-2\cdot x\cdot2+2^2\)

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

c) \(x^2+2x+1-y^2\)

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

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

d) \(x^2-4x\)

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

e) \(x^2+10x+25\)

\(=x^2+2\cdot x\cdot5+5^2\)

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

g) \(x^2-2xy+y^2-9\)

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

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

h) \(2x^2-2\)

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

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

i) \(5x^2-5xy+9x-9y\)

\(=5x\left(x-y\right)+9\left(x-y\right)\)

\(=\left(x-y\right)\left(5x+9\right)\)

k) \(y^2-4y+4-x^2\)

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

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

l) \(x^2-16\)

\(=x^2-4^2\)

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

m) \(3x^2-3xy+2x-2y\)

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

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

o) \(3x^4-6x^3+3x^2\)

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

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

a) 2x² - 2y²

 = (2x - 2y)(2x + 2y)

 = 4(x - y)(x + y)

b) x² - 4x + 4

 = (x - 2)²

c) x² + 2x + 1 - y²

 = (x + 1)² - y²

 = (x + 1 - y)(x + 1 + y)

d) x² - 4x 

 = x(x - 4)

e) x² +10x + 25

 = (x + 5)²

g) x² - 2xy + y² - 9

= (x - y)² - 3²

 = (x - y - 3)(x - y + 3)

h) 2x² - 2

= 2(x² - 1) 

 = 2(x - 1)(x + 1)

i) 5x² - 5xy + 9x - 9y

  = 5x(x - y) + 9(x- y)

 = (5x + 9)(x - y)

k) y² - 4y + 4 - x²

 = (y - 2)² - x²

 = (y - 2 - x)(y - 2 + x)

l) x² - 16

 = x² - 4²

 = (x - 4)(x + 4)

m) 3x² - 3xy + 2x -2y

 = 3x(x - y) +2(x-y)

 = (3x + 2)(x - y)

o) 3x⁴ - 6x³ + 3x²

 = 3x⁴ - 3x³ - 3x³ + 3x²

 = 3x³(x - 1) - 3x²(x - 1)

 = (3x³ - 3x²)(x - 1)

 = 3x²(x - 1)(x - 1)

 = 3x².(x - 1)²

mình đánh máy vội nên sai mn đừng trả lời câu này nha !!!!

a,  x²+2xy+y²+2x+2y-15

<=> (x+y )²+2(x+y)+1-16

Đặt x+y =a

<=> a²+2a+1-4²

<=> (a+1)²-4²

<=> (a+5)(a-3) =>( x+y+5)(x+y-3)

b, x²-4xy+4y²-2x-4y-35

<=> (x-2y)²-2(x-2y)+1-36

Đặt (x-2y)  =b 

=> b²-2b+1-6²

<=> (b-1)²-6²

<=> (b-7)(b+5)=> (x-2y-7)(x-2y+5)

c, 

a,A= x^2+2xy+y^2+2x+2y-15

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

Đặt x+y=a, ta có:

A=a^2+2a-15

  =a^2+2a+1-16

  =(a+1)^2-4^2

  =(a+1+4)(a+1-4)

  =(a+5)(a-3)

Thay a=x+y, ta có: A=(x+y+5)(x+y-3).

b,B= x^2 - 4xy+4y^2-2x-4y-35

   Hình như là sai đề đó bạn. Phải là x^2 - 4xy+4y^2-2x+4y-35 hoặc x^2 - 4xy+4y^2+2x-4y-35 hoặc x^2 + 4xy+4y^2-2x-4y-35 mới đúng đó bạn. Bạn xem lại đi nha.

c,C=6x^4 - 5x^3+8x^2-5x+6

C= x^2(6x^2-5x+8-5/x+6/x^2)

  =x^2(6(x^2+2+1/x^2)-5(x+1/x)-4)

  =x^2(6(x+1/x)^2-5(x+1/x)-4)

Đặt x+1/x=a, ta có:

C=x^2(6a^2-5a-4)

  =x^2(6a^2+3a-8a-4)

  =x^2(2a+1)(3a-4)

Thay a=x+1/x vào là được bạn nhé.

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