27p³-1/216-9/2p²+1/4p

Question

Teresa Woodard

Mathematics

6 September, 22:41

27p³-1/216-9/2p²+1/4p

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Answers (1)

Know the Answer?

Ethen Harrell · Answer 1

Answer: (3p - 1/6) ^3

step-by-step explanation:

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