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

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

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

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

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

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

\(=25x^2-10xy+y^2\)

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

\(=25x^2-10xy+y^2\)

      \(x^3+4x^2+4x+3\)

\(=x^3+3x^2+x^2+3x+x+3\)

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

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

      \(x^2-y^2+4y-4\)

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

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

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

      \(x^4+x^3y-xy^3-y^4\)

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

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

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

Chúc bạn học tốt.

\(x^3+8y^3+2xy^2+x^2y\)

\(=x^3+2x^2y-x^2y-2xy^2+4xy^2+8y^3\)

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

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

ko ai thèm trả lời đâu cu

a) \(4x^2-6x=2x\left(2x-3\right)\)

b) \(9x^4y^3+3x^2y^4=3x^2y^3\left(3x^2+y\right)\)

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

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

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

e) \(5\left(x+3y\right)-15x\left(x+3y\right)=\left(5-15x\right)\left(x+3y\right)\)

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

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

\(=\left(\sqrt{2}x-2\right)\left(\sqrt{2}x+2\right)\left(x+1\right)\)

a,(x-y)^2-2(x+y)+1   b, x^2-y^2+4x+4         c, 4x^2-y^2+8(y-2)

=(x-y-1)^2                  =(x^2+4x+4)-y^2        =4x^2-y^2+8y-16

                                  =(x+2)^2-y^2              =4x^2-(y^2-8y+16)

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

a) (x+y)²-2(x+y)+1=(x+y-1)²

b) x²-y²+4x+4 = (x²+4x+4)-y²=(x+2)²-y²=(x+y+2)(x-y+2)

c)4x²-y²+8(y-2) = 4x²-(y²-8y+16) = (2x)²-(y-4)²=(2x+y-4)(2x-y+4)

d)x³-2x²+2x-4 = x²(x-2)+2(x-2) = (x-2)(x²+2)

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

k) \(x^3-x+3x^2+3xt^2+y^3-y\)

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

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

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

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

h) \(a^3-a^2x-ay+xy\)

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

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

A . 5(x-y)-y(x-y)

=(x6-y)(5-y)

B . x^2 - xy - 8x+8y

=(x^2-xy)-(8x-8y))

=x(x-y) - 8(x-y)

C. x^2-10x+25 - y^2

=(x^2 - 10x + 25 ) - y^2

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

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

D . x^3 - 3x^2-4x+12

=(x^3 - 3x^2 ) - (4x - 12)

=x^2 (x-3)-4(x-3)

=(x^2-4)(x-3)

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

D . 2x^2-2y^2- 6x-6y

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

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

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

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

E . x^3 - 3x^2 + 3x - 1

=(x-1)^3

D.x^2+3x+2

=x^2+2x+x+2

=(x^2+2x)+(x+2)

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

=(x+2)(x+1)

Sai vài chỗ nha bạn! :)

a) y² + 2y = y(y + 2)

b) y³ - 2y² + y = y(y² - 2y + 1) = y(y - 1)²

c) y² - x² - 6y - 6x 

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

<=> (x + y)( y - x - 6)

d) x³ - 3x = x(x² - 3)

e) 2x - xy + 2z - yz 

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

= (2 - y)(x + z)

x²⁺y²-x²y²+xy-x-y=x²-x²y²+y²-y-x+xy

                            =x(1-y²)+y(y-1)-x(1-y)

                            =x²(y-1)(y+1)+y(y-1)+x(y-1)

                           =-x²(y-1)(y+1)+y(y-1)+x(y-1)

                           =(y-1)(-x²(y+1)+y+x)

f)    x⁴+2x²-4x-4=(x³.x+x³.2)-(2x.2+2.2)

                          =x³(x+2)-2(x+2)

                            =(x³-2)(x+2)