27p³-1/216 -9/2p² + 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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Similar questions

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

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

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

Factorise: 27p³-1/216-9/2p²+1/4

(i) 8 a^{3} + b^{3} + 12 a^{2} b + 6 a b^{2} (i i) 8 a^{3} - b^{3} - 12 a^{2} b + 6 a b^{2} (i i i) 27 - 125 a^{3} - 135 a + 225 a^{2} (v i) 64 a^{3} - 27 b^{3} - 144 a^{2} b + 108 a b^{2} (v) 27 p^{3} - \frac{1}{216} - \frac{9}{2} p^{2} + \frac{1}{4} p

Factorise each of the following:

(i) (ii)

(iii) (iv)

(v)

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