a) Ta có: \(x^2-2xy+y^2-2x+2y\)

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

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

b) Ta có: \(x^2-4x+4-x^2y+2xy\)

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

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

c) Ta có: \(ax^2-3axy-x^2+6xy-9y^2\)

\(=ax\left(x-3y\right)-\left(x^2-6xy+9y^2\right)\)

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

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

d) Ta có: \(2a^2x-5a^2y-4x^2+30xy-25y^2\)

\(=a^2\left(2x-5y\right)-\left(4x^2-30xy+25y^2\right)\)

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

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

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

??? đề bài

a: 2x^2y-50xy=2xy(x-25)

b: 5x^2-10x=5x(x-2)

c: 5x^3-5x=5x(x^2-1)=5x(x-1)(x+1)

d: \(x^2-xy+x=x\left(x-y+1\right)\)

e: x(x-y)-2(y-x)

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

=(x-y)(x+2)

f: 4x^2-4xy-8y^2

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

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

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

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

f1: x^2ỹ-y^2+y

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

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

\(a,=2\left(xy^2-2\right)\\ b,=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x-y+1\right)\left(x+y\right)\\ c,=y\left(x^2-6x-9\right)\\ d,=x^2+3x+x+3=x\left(x+3\right)+\left(x+3\right)=\left(x+1\right)\left(x+3\right)\)

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

b) x^2 -y^4+9y -x(9+y-y^3= x^2-y^4 +9y-9x-xy+xy^3=  (x^2-xy)-(9x-9y)+(xy^3-y^4)=x(x-y)-9(x-y)+y^3(x-y)=(x-y)*(y^3+x-9)

d) 2u^2+2v^2-5uv=(2u^2-4uv)+(2v^2-uv)=2u(u-2v)+v(2v-u)= 2u(u-2v)-v(u-2v)=(u-2v)*(2u-v)

1: \(=a\left(x+y\right)-4\left(x+y\right)=\left(x+y\right)\left(a-4\right)\)

2: \(=x\left(x+b\right)+a\left(x+b\right)=\left(x+b\right)\left(x+q\right)\)

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

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

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