Question

math solve this question

Answer 1

LHS=
${a}^{3} + {b}^{3}$
RHS=
$(a + b) ({a}^{2} - ab + {b}^{2} )$
Finding product of RHS,
$= a( {a}^{2} -ab + b {}^{2} ) + b( {a}^{2} - ab + {b}^{2} ) \\ = a {}^{3} - {a}^{2} b + ab {}^{2} + {a}^{2} b - ab {}^{2} + b {}^{3} \\ = a {}^{3} + b {}^{3}$
LHS=RHS
-----verified------


NOW FACTORISE-----:
$x {}^{3} y {}^{3} + \frac{1}{512}$
We can factorise this using above identity,
So,
$(xy) {}^{3} + ( \frac{1}{5} ) {}^{3}$
Now, this is in the form of above identity
$a {}^{3} + b {}^{3} = (a + b )\: ({a}^{2} - ab + b {}^{2} )$
So,
$(xy + \frac{1}{8} )( \: (xy) {}^{2} - xy \times \frac{1}{8} + ( \frac{1}{8} ) {}^{2} \: ) \\ = (xy + \frac{1}{8} )(x {}^{2} y {}^{2} - \frac{xy}{8} + \frac{1}{64} )$
Hope this will help you.