Question

Workout the following divisions
$54lmn(l+m)(m+n)(n+1)÷81mn(l+m)(n+l)$

• A. $\frac{2}{3}l(m+n)$
• B. $\frac{2}{3}(m+n)$
• C. $\frac{2}{3}l(m-n)$
• D. None

Answer 1

Answer: (A)

$\frac{2}{3}l(m+n)$

We divide the given polynomial $54lmn(l+m)(m+n)(n+l)$ by $81mn(l+m)(n+l)$ as shown below:

$\frac{54lmn(l+m)(m+n)(n+l)}{81mn(l+m)(n+l)}=\frac{54}{81}\times \frac{lmn}{mn}\times \frac{(l+m)(m+n)(n+l)}{(l+m)(n+l)}=\frac{2\times 3\times 3\times 3}{3\times 3\times 3\times 3}\times \frac{lmn}{mn}\times \frac{(l+m)(m+n)(n+l)}{(l+m)(n+l)}=\frac{2}{3}\times l\times (m+n)=\frac{2}{3}l(m+n)$

Hence, $\frac{54lmn(l+m)(m+n)(n+l)}{81mn(l+m)(n+l)}=\frac{2}{3}l(m+n)$.