Question

factorise
please help me​

Answer 1

Step-by-step explanation:

$\frac{1}{27 } {p}^{3} - \frac{1}{8} {q}^{3}$

$( \frac{1}{ {3} } p) ^{3} - ( \frac{1}{2} q) ^{3}$

We know that

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

$( \frac{1}{3} p) ^{3} - ( \frac{1}{2} q) ^{3} = ( \frac{1}{3} p - \frac{1}{2} q) \\ (( \frac{1}{3} p) ^{2} + \frac{1}{3} p \times \frac{1}{2} q + ( \frac{1}{2} q) ^{2})$

$\: \: \: \: \: \:: \: \: \: \: \: \: = ( \frac{1}{3} p - \frac{1}{2} q)( \frac{1}{9 } {p}^{2} + \frac{1}{6} pq + \frac{1}{4} {q}^{2} )$