Question

Divide the following by 6abc:
$30\left( {{a^2}bc + a{b^2}c + ab{c^2}} \right)$

Answer 1

Hint: In this question $30\left( {{a^2}bc + a{b^2}c + ab{c^2}} \right)$ will be the numerator part and 6abc will be the denominator one. Take the terms out which are common in both the numerator and the denominator part in order to get them cancelled.

Complete step-by-step answer:

Given equation is
$30\left( {{a^2}bc + a{b^2}c + ab{c^2}} \right)$........................... (1)
Now we have to divide this equation by 6abc.
So take abc common from equation (1) we have,
$ \Rightarrow 30\left( {{a^2}bc + a{b^2}c + ab{c^2}} \right) = 30abc\left( {a + b + c} \right)$
Now divide this equation by 6abc we have,
$ \Rightarrow \dfrac{{30abc\left( {a + b + c} \right)}}{{6abc}}$
Now as we see abc is cancel out from numerator and denominator and 30 is cancel out from 6 by 5 times so the remaining term are
$ \Rightarrow 5\left( {a + b + c} \right)$
So this is the required value when $30\left( {{a^2}bc + a{b^2}c + ab{c^2}} \right)$ is divided by 6abc.
So this is the required answer.

Note: In division the number that is divided is called the dividend and the number by which dividend is being divided by is called the divisor. The answer thus obtained to a division problem is called a quotient.