`a)`
`3xy(x - 5) - 6x(5 - x)`
`= 3xy(x - 5) + 6x(x - 5)`
`= (x - 5)(3xy + 6x)`
`= (x - 5) . 3x(y + 2)`
`b)`
`3x^2(x + 1)^2 - x(x + 1)^3`
`= (x + 1)^2(3x^2 - x(x + 1))`
`= (x + 1)^2 . x(3x - x - 1)`
`c)`
`x^2 - x + 1/4`
`= x^2 - 2 . x . 1/2 + 1/4`
`= (x - 1/2)^2`
`d)`
`8x^3 - 1/8`
`= (2x)^3 - (1/2)^3`
`= (2x - 1/2)(4x^2 + x + 1/4)`