x2 + 4x – 2xy – 4y + y2 = (x2-2xy+ y2) + (4x – 4y) → bạn Việt dùng phương pháp nhóm hạng tử

= (x - y)2 + 4(x – y) → bạn Việt dùng phương pháp dùng hằng đẳng thức và đặt nhân tử chung

= (x – y)(x – y + 4) → bạn Việt dùng phương pháp đặt nhân tử chung

\(a,=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\\ b,=\left(x+y\right)\left(x-5\right)\\ c,=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-2y\right)\left(x-y\right)\\ d,=x^2-2xy=x\left(x-2y\right)\\ e,=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

a) 3(x-y) - (x-y)^2

 =(x-y)(3-x+y)

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

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

\(a,=3\left(x-y\right)-\left(x-y\right)^2=\left(x-y\right)\left(3-x+y\right)\\ b,=\left(x+y\right)^2-4x^2y^2=\left(x-2xy+y\right)\left(x+2xy+y\right)\\ c,=\left(x+y-x+y\right)\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\\ =2y\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\\ =2y\left(3x^2+y^2\right)\\ d,=x^2+2x-7x-14=\left(x+2\right)\left(x-7\right)\)

Lời giải:
$\frac{x}{y}$ không phải đơn thức bạn nhé.

a. $x^2-2x+1=(x-1)^2$

b. $x^2+2xy-25+y^2=(x^2+2xy+y^2)-25=(x+y)^2-5^2=(x+y-5)(x+y+5)$

c. $5x^2-10xy=5x(x-2y)$

d. $x^2-y^2+x-y=(x^2-y^2)+(x-y)=(x-y)(x+y)+(x-y)$

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

a: Ta có: \(x^2-xy-3x+3y\)

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

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

b: Ta có: \(5x^2+5xy-x-y\)

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

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

c: Ta có: \(x^2-2xy+y^2-z^2\)

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

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

x 2  – 2xy +  y 2  -  z 2

      = ( x 2  – 2xy +  y 2 ) –  z 2

      = x - y 2  –  z 2

      = (x – y + z)(x – y – z)

a) \(=x^2+7x-12x-84-2x+14\)

\(=x^2-7x-70\)

b)\(=x^2-4x-2x+8\)

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

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

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

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

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

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

e)\(=x^2+8x+16-60+15x\)

\(=x^2+23x-44\)

a) Ta có: \(\left(x-12\right)\left(x+7\right)-2x-14\)

\(=\left(x-12\right)\left(x+7\right)-2\left(x+7\right)\)

\(=\left(x+7\right)\left(x-14\right)\)

b) Ta có: \(x^2-6x+8\)

\(=x^2-2x-4x+8\)

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

c) Ta có: \(9x^2+9xy-\left(x+y\right)\)

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

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

d) Ta có: \(\left(x^2-2xy+y^2\right)-81\)

\(=\left(x-y\right)^2-81\)

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