Question

Rearrange the like terms:
$7l^3{m}^2-21l{m}^{2}n+28lm$

Answer 1

The given terms $7l^3{m}^2,21l{m}^{2}n$ and $28lm$ can be rewritten as follows:

$7l^3{m}^2=7\times l\times l\times l\times m\times m21l{m}^{2}n=7\times 3\times l\times m\times m\times n28lm=7\times 4\times l\times m$

These terms have $7,l$ and $m$ as common factors, therefore,

$7l^3{m}^2-21l{m}^{2}n+28lm=(7\times l\times l\times l\times m\times m)-(7\times 3\times l\times m\times m\times n)+(7\times 4\times l\times m)=7\times l\times m\left[\right(l\times l\times m)-(3\times m\times n)+(4\left)\right]\left(Combiningliketerms\right)=7lm(l^{2}m-3mn+4)$

Hence, $7l^3{m}^2-21l{m}^{2}n+28lm=7lm(l^{2}m-3mn+4)$.