Question

Factorize : 125p3 + 27q3 . Also, mention the identity used here.

Answer 1

$125p {}^{3} + 27q {}^{3} \\ = (5p) {}^{3} + (3q) {}^{3} \\ = (5p + 3q) \: ( \: (5p) {}^{2} - (5p)(3q) + (3q) {}^{2} \: ) \\ = (5p + 3q)(25p {}^{2} - 15pq + 9q {}^{2} )$