Question

factorise 1/27 p³-8q³​

Answer 1

Answer:

$( \frac{p}{3} - 2q)( \frac{ {p}^{2} }{9} + \frac{2pq}{3} + {4q}^{2} )$

Step-by-step explanation:

$\frac{p ^{3} }{27} - 8q ^{3} \\ = )( \frac{p}{3} )^{3} - (2q^{3} ) \\ since \: {a}^{3} - {b}^{3} = (a + b)( {a}^{2} + ab + {b}^{2} ) \\ = )( \frac{p}{3} - 2q)(( \frac{p}{3} )^{2} + \frac{p}{3} \times 2q + {2q}^{2}) \\ = )( \frac{p}{3} - 2q)( \frac{p^{2} }{9} + \frac{2pq}{3} + 4q ^{2} )$

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