`1)`
`a)x(x-y)+3x-3y`
`=x(x-y)+3(x-y)`
`=(x+3)(x-y)`
`b)x^2-9y^2`
`=x^2-(3y)^2`
`=(x-3y)(x+3y)`
`c)x^2-y^2+4x+4`
`=x^2+4x+4-y^2`
`=(x+2)^2-y^2`
`=(x+2-y)(x+2+y)`
`3)`
`a)x(x+1)-x(x-3)=0`
`⇒x^2+x-x^2+3x=0`
`⇒4x=0`
`⇒x=0`
`b)x^2-6x+8=0`
`⇒x^2-4x-2x+8=0`
`⇒x(x-4)-2(x-4)=0`
`⇒(x-2)(x-4)=0`
`⇒` \(\left[ \begin{array}{l}x-2=0\\x-4=0\end{array} \right.\)
`⇒` \(\left[ \begin{array}{l}x=2\\x=4\end{array} \right.\)