factorise 27p^3-1/216-9/2p^2+1/4p

Question

please solve with steps...thanx

Answer 1

27p^3 - 1/216 - 9/2p^2 + 1/4p

= (3p)^3 - (1/6)^3 - 9/2p^2 + 1/4p

= (3p - 1/6)[(3p)^2 + p/2 + 1/36)] - (3p/2)(3p - 1/6)

= (3p - 1/6)(9p^2 + p/2 + 1/36 - 3p/2)

= (3p - 1/6)(9p^2 - 2p/2 + 1/36)

= (3p - 1/6)(9p^2 - p + 1/36)

= (3p - 1/6)(3p - 1/6)(3p - 1/6)

= (3p - 1/6)^3

you can thank me now 3:D