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

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Solution

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

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Factorize: $27 p^{3} - \frac{1}{216} - \frac{9}{2} p^{2} + \frac{1}{4} p$

27p³-1/216 -9/2p² + 1/4p

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= (3 p - \frac{1}{6}) (3 p - \frac{1}{6}) (3 p - \frac{1}{6})

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