5x² - 10xy + 5y² - 20z²

=5(x² - 2xy + y² - 4z²)

= 5[ (x² - 2xy + y²) - (2z)²]

= 5[(x-y)² - (2z)²]

= 5(x-y-2z)(x-y+2z)

5x²-10xy+5y²-20z²

=5(x²-2xy+y²-4z²)

=5[(x-y)²-(2z)²]

=5(x-y-2z)(x-y+2z)

x² - y² - x-y

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

=(x+y)(x-y-1) 

x²-y²-2xy+y²

=x²-2xy

=x(x-2y)

x² - y² - 2xy + y²

= (x² - 2xy +y²) - y²

= (x-y)² - y²

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

= x(x-2y)

27x³-8y³

=(3x)³-(2y)³

=(3x-2y)(9x²+6xy+4y²)

\(27x^3-8y^3=\left(3x\right)^3-\left(2y\right)^3=\left(3x-2y\right)\left(9x^2+6xy+4y^2\right)\)

x⁶-y⁶

=(x³-y³)(x³+y³)

=(x-y)(x²+xy+y²)(x+y)(x²-xy+y²)

x^6-y^6=(x^3)^2 - (y^3)^2 = (x^3+y^3)(x^3 - y^3) = (x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)

\(5x^3-5x^2y-10x^2+10xy=5x^2\left(x-y\right)-10x\left(x-y\right)=5x\left(x-2\right)\left(x-y\right)\)

ta có :

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

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

x²-5x+5y-y²

=(x²-y²)-(5x-5y)

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

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

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

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

=(x+y)(x-5)

1) ( x - 2 ) ( x² + 2x +4 )=\(x^3-8\)

2) ( x+4) ( x² - 4x + 16 ) \(=x^3+64\)

3) ( x - 3y ) (x² + 3xy + 9y²  ) \(=x^3-27y^3\)

4) ( x² - 1/3 ) ( x⁴ + 1/3x² + 1/9 ) \(=x^6-\frac{1}{27}\)