Question

factories a³-125/a³ ​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO FACTORISE

$\displaystyle \sf{ {a}^{3} - \frac{125}{ {a}^{3} } \: }$

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

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

CALCULATION

$\displaystyle \sf{ {a}^{3} - \frac{125}{ {a}^{3} } \: }$

$= \displaystyle \sf{ {(a)}^{3} - {\bigg(\frac{5}{ a } \bigg) }^{3} \: }$

$= \displaystyle \sf{ \bigg (a - \frac{5}{a} \bigg) \:\bigg [ {a}^{2} + a \times \frac{5}{a} + { \bigg( \frac{5}{a} \bigg)}^{2} \bigg] }$

$= \displaystyle \sf{ \bigg (a - \frac{5}{a} \bigg) \:\bigg( {a}^{2} + 5 + { \frac{25}{ {a}^{2} } } \bigg) }$

RESULT

$\boxed{ \displaystyle \sf{ \: {a}^{3} - \frac{125}{ {a}^{3} } \: } = \bigg (a - \frac{5}{a} \bigg) \:\bigg( {a}^{2} + 5 + { \frac{25}{ {a}^{2} } } \bigg) \: \: }$

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