Question

Please help. Answer the attached question please.

Answer 1

${3p}^{3} - \frac{1}{ {6}^{3} } - 3 {(3p)}^{2} \times \frac{1}{6} + 3(3 p) \times \frac{1}{ {(6)}^{2} } \\ cubic \: equation \\ {(3p - \frac{1}{6} )}^{ 3 }$

Answer 2

the question can be written as
(3p) ^3 -(1/6)^3 -9/2p^2 +1/4*3/3p
(3p) ^3 -(1/6)^3 -3/2p(3p-1/6)
(3p) ^3 -(1/6)^3 - 3/2*3/3p(3p-1/6)
(3p) ^3 -(1/6)^3 -3*3p*1/6(3p-1/6)
clearly this is of the form
(a-b) ^3 = a^3-b^3-3ab(a-b)
were a=3p , b=4/6
so this can be written as
(3p-1/6)^3
hence this is the factorised form of the given equation
hope it helps you