`a)36xy^3-12x^2y^2`
`=12xy^2*3y-12xy^2*x`
`=12xy^2*(3y-x)`
`b)x^2-x+1/4`
`=x^2-2*x*1/2+(1/2)^2`
`=(x-1/2)^2`
`c)a^2x+a^2y-7x-7y`
`=a^2(x+y)-7(x+y)`
`=(a^2-7)(x+y)`
`d)3x^2y-9xy^2+12x^2y^2`
`=3xy*x-3xy*3y+3xy*4xy`
`=3xy(x-3y+4xy)`
`e)x^3-6x^2y+12xy^2-8y^3`
`=x^3-3*x^2*2y+3*x*(2y)^2-(2y)^3`
`=(x-2y)^3`