a: =(x-3)(x-1)(x+1)

A

a/ \(x^3-3x^2-x+3\)

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

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

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

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

b/ \(x^2y-2xy^2+y^3\)

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

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

Giải thích: `x^2-5x+1`

`=x^2-2. 5/2x+25/4-21/4`

`=(x-5/2)^2-21/4`

`=(x-5/2-\sqrt{21}/2)(x-5/2+\sqrt{21}/2)`

`=(x-[5+\sqrt{21}]/2)(x-[5-\sqrt{21}]/2)`

-3x⁴y + 6x³y - 3x²y

= -3x²y( x² - 2x + 1 )

= -3x²y( x - 1 )²

-3x⁴y+6x³y-3x²y

=-3x²y(x²-2xy+1)

=-3x²y(x-1)²

a) \(x^2-2xy+y^2-xz+yz\) 

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

= \(\left(x-y\right)\left(x-y-z\right)\)

b) \(x^3+9x^2-4x-36\)

= \(x^3-2x^2+11x^2-22x+18x-36\)

= \(x^2\left(x-2\right)+11x\left(x-2\right)+18\left(x-2\right)\)

= \(\left(x-2\right)\left(x^2+11x+18\right)\)

= \(\left(x-2\right)\left(x^2+2x+9x+18\right)\)

= \(\left(x-2\right)\left(x+2\right)\left(x+9\right)\)

Chuc ban hoc tot

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

b: =x(x^2-2x+1+4y^2)

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

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

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

3x - 3y + x² - y² 

= (3x - 3y) + (x² - y²)

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

=(3 + x + y)(x - y)

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

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

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

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

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