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

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

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

`x^2 -4x+4-y^2`

`=(x^2 -4x+4)-y^2`

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

`=(x-2-y)(x-2+y)`

`x^2+2xy+y^2-x-y`

`=(x^2+2xy+y^2) -(x+y)`

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

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

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

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

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

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

Tách ra đi cậu.

\(x^2-2xy+y^2+3x-3y-4\)

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

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

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

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

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

\(=\left(x-y-1\right)\left(x-y+4\right)\)

x²-x-y²-y=(x²-y²)-(x+y)=(x-y)(x+y)-(x+y)=(x+y)(x-y-1)

x²-xy+x-y=x(x-y)+(x-y)=(x+1)(x-y)

1. (x-3)²

2. (3y+2x)²

3. (1/5x-8y)(1/5x+8y)

4. (x-2y)(x²+2xy+4y²)

5. (4x-3-x-1)(4x-3+x+1)

(3x-4)(5x-2)

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

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

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

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

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

\(=3x^2-3y^2-2x^2+4xy-2y^2\)

\(=x^2+4xy-5y^2\)

\(=x^2+4xy+4y^2-9y^2\)

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

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

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