\(x^6-x^4-9x^3+9x^2\)

\(\left(x^6-x^4\right)-\left(9x^3-9x^2\right)\)

\(x^4\left(x^2-x\right)-9x\left(x^2-x\right)\)

\(\left(x^2-x\right)\left(x^4-9x\right)\)

(x-1)*x^2*(x^3+x^2-9)

x⁴(x² - 1) - 9x²(x - 1)

=x⁴(x - 1)(x + 1) - 9x²(x -1)

=(x - 1)(x⁵ + x⁴ - 9x²)

= x⁴(x²-1)-9x²(x-1)

=x⁴(x-1)(x+1)-9x²(x-1)

=(x⁴(x+1)-9x²)(x-1)

=(x⁵+x⁴-9x²)(x-1)

`@` `\text {Ans}`

`\downarrow`

`4x^3 - 4x^2 - 9x + 9`

`= (4x^3 - 4x^2) - (9x - 9)`

`= 4x^2(x - 1) - 9(x - 1)`

`= (4x^2 - 9)(x - 1)`

____

`x^3 + 6x^2 + 11x + 6`

`= x^3 + x^2 + 5x^2 + 5x + 6x + 6`

`= (x^3 + x^2) + (5x^2 + 5x) + (6x + 6)`

`= x^2*(x + 1) + 5x(x + 1) + 6(x + 1)`

`= (x^2 + 5x + 6)(x+1)`

____

`x^2y - x^3 - 9y + 9x`

`= (x^2y - 9y) - (x^3 - 9x)`

`= y(x^2 - 9) - x(x^2 - 9)`

`= (y - x)(x^2 - 9)`

b: =x^3+x^2+5x^2+5x+6x+6

=(x+1)(x^2+5x+6)

=(x+1)(x+2)(x+3)

c: =x^2(y-x)-9(y-x)

=(y-x)(x^2-9)

=(y-x)(x-3)(x+3)

a: =(4x^3-4x^2)-(9x-9)

=4x^2(x-1)-9(x-1)

=(x-1)(4x^2-9)

=(x-1)(2x-3)(2x+3)

\(x^6-x^4-9x^3+9x^2\)

\(=x^6-x^5+x^5-x^4-9x^2\left(x-1\right)\)

\(=x^5\left(x-1\right)+x^4\left(x-1\right)-9x^2\left(x-1\right)\)

\(=\left(x-1\right)\left(x^5+x^4-9x^2\right)\)

\(x^6-x^4-9x^3+9x^2\)

\(=x^4.\left(x^2-1\right)-9x^2\left(x-1\right)\)

\(=x^4.\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)

\(=\left(x-1\right)\left[x^4.\left(x+1\right)-9x^2\right]\)

\(=\left(x^5+x^4\right)\left(x-1\right)-\left(3x\right)^2\left(x-1\right)\)

\(=\left(x-1\right)\left(x^5+x^4-9x^2\right)\)

\(=\left(x-1\right)\left[x^5+x^2\left(x^2-3^2\right)\right]\)

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

x⁶ - x⁴ - 9x³ + 9x²

= x⁴.(x² - 1) - 9x².(x - 1)

= x⁴.(x - 1).(x + 1) - 9x².(x - 1)

= (x - 1).(x⁵ + x - 9x²)

= (x - 1).x.(x⁴ + 1 - 9x)

x^6-x^4-9x^3+9x^2

=x^2(x^4-x^2-9x+9)

=x^2[x^2(x^2-1)-9(x-1)]

=x^2[x^2(x-1)(x+1)-9(x-1)]

=x^2(x-1)[x^2(x+1)-9)]

=x^2(x-1)(x+1)(x^2-9)

=x^2(x-1)(x+1)(x-3)(x+3)

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

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

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

c) \(x^4-4x^3+8x^2-16x+16=x^4+8x^2+16-\left(4x^3+16x\right)\)

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

b) \(x^6-x^4-9x^3+9x^2=x^4\left(x^2-1\right)-\left(9x^3-9x^2\right)\)

\(=x^4\left(x-1\right)\left(x+1\right)-9x^2\left(x-1\right)\)

\(=\left(x^5+x^4-9x^2\right)\left(x-1\right)=\left(x-1\right)x^2\left(x^3+x^2-9\right)\)

\(b,=x^4-2x^3-x^3+2x^2+3x^2-6x-3x+6\\ =\left(x-2\right)\left(x^3-x^2+3x-3\right)\\ =\left(x-2\right)\left(x-1\right)\left(x^2+3\right)\\ c,=x^4-2x^3+4x^3-8x^2+4x^2-8x+3x-6\\ =\left(x-2\right)\left(x^3+4x^2+4x+3\right)\\ =\left(x-2\right)\left(x^3+3x^2+x^2+3x+x+3\right)\\ =\left(x-2\right)\left(x+3\right)\left(x^2+x+1\right)\)

\(1-27x^3\)

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

\(=\left(1-3x\right)\left(1+3x+9x^2\right)\)

\(---\)

\(x-3^3+27\)

\(=x-27+27=x\) 

\(---\)

\(27x^3+27x^2+9x+1\)

\(=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2+1^3\)

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

\(---\)

\(\dfrac{x^6}{27}-\dfrac{x^4y}{3}+x^2y^2-y^3\) (sửa đề)

\(=\left(\dfrac{x^2}{3}\right)^3-3\cdot\left(\dfrac{x^2}{3}\right)^2\cdot y+3\cdot\dfrac{x^2}{3}\cdot y^2-y^3\)

 \(=\left(\dfrac{x^2}{3}-y\right)^3\)

#Ayumu

1-27x\(^3\)

=(1-3x)(1+3x+9x\(^2\)