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 ) \(=x^6-\frac{1}{27}\)

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

x-y²+x²-y

=(x-y)+(x²-y²)

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

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

ta có :

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

x⁴-x³-x²+1

=x³(x-1)-(x²-1)

=x³(x-1)-(x-1)(x+1)

=(x-1)(x³-x-1)

x⁴ + x³ + x +1

= x³(x+1) + (x+1)

=(x+1)(x³ +1)

= (x+1)(x+1)(x² - x-1)

= (x+1)²(x² -x+1) 

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

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

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

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

(-x+6)(-x-2)

= -(x-6) . [- (x+2)]

= (x-6)(x+2)

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

= x² + 2x - 6x - 12

= x² - 4x -12

(2x-3)(5-x)

=2x(5-x) - 3(5-x)

= 10x - 2x² - 15 + 3x

= -2x² - 15 + 13x

\(\left(2x-3\right)\left(5-x\right)=10x-2x^2-15+3x\)

\(=13x-2x^2-15\)

x³ - 3x² - 4x + 12

= x²(x-3) - 4(x-3)

= (x-3)(x² -4)

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

\(x^3-3x^2-4x+12\)

\(=\left(x^3-3x^2\right)-\left(4x-12\right)\)

\(=x^2\left(x-3\right)-4\left(x-3\right)\)

\(=\left(x^2-4\right)\left(x-3\right)\)

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