Divide $30 (a^{2} b c + a b^{2} c + a b c^{2})$ by $6 a b c$

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Solution

$30 (a^{2} b c + a b^{2} c + a b c^{2})$
$= 2 \times 3 \times 5 [(a \times a \times b \times c) + (a \times b \times b \times c) + (a \times b \times c \times c)]$
$= 2 \times 3 \times 5 \times a \times b \times c (a + b + c)$
Thus $30 (a^{2} b c + a b^{2} c + a b c^{2}) \div 6 a b c$
$= \frac{2 \times 3 \times 5 \times a b c (a + b + c)}{2 \times 3 \times a b c}$
$= 5 (a + b + c)$
Alternatively $30 (a^{2} b c + a b^{2} c + a b c^{2}) \div 6 a b c$
$= \frac{30 a^{2} b c}{6 a b c} + \frac{30 a b^{2} c}{6 a b c} + \frac{30 a b c^{2}}{6 a b c}$
$= 5 a + 5 b + 5 c$
$= 5 (a + b + c)$

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