a) ${ 2x^2-6x}$
${ = 2x.(x-3)}$
b) ${ 2x^2 - 18}$
${ = 2.(x^2-9)}$
${ = 2.(x^2-3^2)}$
${ = 2.(x-3).(x+3)}$
c) ${ x^3 + 3x^2 + x + 3}$
${ =x^2.(x+3)+(x+3)}$
${ = (x^2+1).(x+3)}$
d) ${ x^2 - y^2 + 6y - 9}$
${ = x^2-(y^2-6y+9)}$
${ = x^2-(y^2-2.3.y+3^2)}$
${ = x^2-(y-3)^2}$
${ = (x-y+3).(x+y-3)}$