Question

Factorize:
$64a^3+125b^3+240a^{2}b+300a{b}^2$

Answer 1

Given:$64a^3+125b^3+240a^{2}b+300a{b}^2$
$\therefore 64a^3+125b^3+240a^{2}b+300a{b}^2$
$=(4a{)}^3+(5b{)}^3+3\times (4a{)}^2\times (5b)+3\times (4a)\times (5b{)}^2$

$=(4a+5b{)}^3$

$[\therefore a^3+b^3+3a^{2}b+3a{b}^2=(a+b{)}^3]$

$=(4a+5b)(4a+5b)(4a+5b)$

Hence,$64a^3+125b^3+240a^{2}b+300a{b}^2=(4a+5b)(4a+5b)(4a+5b).$