27p3-8
Rewrite 27p3 as (3p)3.
(3p)3-8
Rewrite 8 as 23.
(3p)3-23
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=3p and b=2.
(3p-2)((3p)2+3p⋅2+22)
Apply the product rule to 3p.
(3p-2)(32p2+3p⋅2+22)
Raise 3 to the power of 2.
(3p-2)(9p2+3p⋅2+22)
Multiply 2 by 3.
(3p-2)(9p2+6p+22)
Raise 2 to the power of 2.
(3p-2)(9p2+6p+4)
(3p-2)(9p2+6p+4)
Factor 27p^3-8
