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

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

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

2x2 + 4x + 2 – 2y2 (có nhân tử chung là 2)

= 2.(x2 + 2x + 1 – y2) (Xuất hiện x2 + 2x + 1 là hằng đẳng thức)

= 2[(x2 + 2x + 1) – y2]

= 2[(x + 1)2 – y2] (Xuất hiện hằng đẳng thức (3))

= 2(x + 1 – y)(x + 1 + y)

\(a,x^2-2xy+y^2-z^2=\left(x-y\right)^2-z^2=\left(x-y-z\right).\left(x-y+z\right)\)

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

a) \(=3\left(5y+4x\right)\)

b) \(=\left(x-3\right)^2\)

c) \(=y\left(y^2+2y+3\right)\)

d) \(=x\left(x+y\right)+6\left(x+y\right)=\left(x+6\right)\left(x+y\right)\)

2x² - 2y² - 6x - 6x = 2(x² - y²) - 6(x + y) = 2(x - y)(x + y) -2.3.(x + y) = 2(x + y)[(x - y) - 3] = 2(x + y)(x - y - 3)    

\(=x\left(x-6\right)+y\left(x-6\right)=\left(x+y\right)\left(x-6\right)\)

a)2x^2+xy-y^2-x+2y-1

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

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

=2a^2+ab-b^2         với a=x,b=y-1

=2a^2+2ab-ab-b^2

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

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