Question

a^3-1/3^3 identity.....

Answer 1

Since , we know that ,

a³ – b³ = (a – b) (a² + ab + b² ).

so ,

${(a)}^{3} - ( \frac{1}{ {3} })^{3} \\ \\ =( a - \frac{1}{3} )( {(a)}^{2} + a \times \frac{1}{3} + ( { \frac{1}{3}) }^{2} ) \\ \\ = ( a - \frac{1}{3} )( {a}^{2} + \frac{a}{3} + \frac{1}{9} )$

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Answer 2

Question : Solve a^3 - 1/3^3 using the identities.

Step by step explanation :

We already know that,

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

Here,

$\tt \small{a {}^{3} - {b}^{3} = (a- \frac{1}{3} )(a {}^{2} + a \times \frac{1}{3} + (\frac{1}{3}) {}^{2}) }$

$\tt {= (a - \frac{1}{3})( {a}^{2} + \frac{a}{3} + \frac{1}{9}} )$

Thus,

Answer to your question is as follows :

$\tt {= (a - \frac{1}{3})( {a}^{2} + \frac{a}{3} + \frac{1}{9}} )$