Question

Factorize the following expression:
$p^3+27$

Answer 1

Given: $p^3+27$

$\therefore p^3+27$
$=p^3+3^3$
$=(p+3)(p^2-3p+3^2)$
$[\therefore a^3+b^3=(a+b\left)\right(a^2-ab+b^2\left)\right]$
$=(p+3)(p^2-3p+9)$

Hence, $p^3+27=(p+3)(p^2-3p+9)$.