het thoirui pan oi

b) x⁴+2007x²+2006x+2007

=x⁴-x+2007x²+2007x+2007

=x.(x³-1)+2007.(x²+x+1)

=x.(x-1)(x²+x+1)+2007.(x²+x+1)

=(x²+x+1)(x²-x+2007)

a: \(4x^2-12x+9-3\left(2x-3\right)\left(x+1\right)\)

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

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

\(=-\left(x+6\right)\left(2x-3\right)\)

b: \(25-4x^2+8xy-4y^2\)

\(=25-\left(2x-2y\right)^2\)

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

cảm ơn anh ạ

6B, 7A, 8D

a.

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

b.

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

c.

\(27+27x+9x^2+x^3=x^3+3.x^2.3+3.3^2.x+3^3\)

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

d.

\(2x^3+4x^2+2x=2x\left(x^2+2x+1\right)=2x\left(x+1\right)^2\)

e.

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

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

f.

\(x^2-6x+9-y^2=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)

g. 10x(x-y)-6y(y-x)

=10x(x-y)+6y(x-y)

=(x-y)(10x+6y)

h.x²-4x-5

=(x-5)(x+1)

i.x⁴-y⁴ = (x²-y²)(x²+y²)

Ta có : 5x³ - 45x

= 5x(x² - 9)

= 5x(x - 3)(x + 3)

b ) Ta có : 3x² - 7x - 6 

= 3x² - 9x + 2x - 6 

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

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

b) a³ + b³ + c³ - 3abc

= ( a + b)³ - 3ab - 3ba + c - 3abc

= (a³ + 3a²b + 3ab² + b³) + c³ - (3a²b + 3ab² + 3ab) 

= (a + b)³ + c² - 3ab(a + b + c)

= (a + b + c) [ (a  + b)² - ( a + b )c + c^2 ]  - 3ab(a + b + c)

=  ( a + b + c ) ( a² + b² + 2ab - ac - bc + c² -3ab )

=  ( a + b + c ) ( a² + b² + c² - ab - ac - bc