Question

Simplify: $\left(P+\frac{P}{3}\right)\left(2P+\frac{P}{2}\right)\left(3P-\frac{2P}{3}\right)$

Answer 1

Consider the given expression.

$(P+\frac{P}{3})(2P+\frac{P}{2})(3P-\frac{2P}{3})$

$=\left(\frac{3P+P}{3}\right)\left(\frac{4P+P}{2}\right)\left(\frac{9P-2P}{3}\right)$

$=\left(\frac{4P}{3}\right)\left(\frac{5P}{2}\right)\left(\frac{7P}{3}\right)$

$=\frac{70P^3}{9}.$

Hence, the value is $\frac{70P^3}{9}.$