`a)`
`3x^2-6xy+3y^2`
`=3(x^2-2xy+y^2)`
`=3(x-y)^2`
`b)`
`12x^5y+24x^4y^2+12x^3y^3`
`=12x^3y(x^2+2xy+y^2)`
`=12x^3y(x+y)^2`
`c)`
`64xy-96x^2y+48x^3y-8x^4y`
`=8(8xy-12x^2y+6x^3y-x^4y)`
`=8[xy(8-12x+6x^2-x^3)]`
`=8[xy*-(x^3-6x^2+12x-8)]`
`=8[xy*-(x-2)^3]`
`=-8xy(x-2)^3`
`d)`
`54x^3+16y^3`
`=2(27x^3+8y^3)`
`=2[(3x)^3+(2y)^3]`
`=2[(3x+2y)(9x^2-6xy+4y^2)]`