Solve +12pq+4q^2/9pq*p^2q/27p^2+18pq

$$\frac { + 12 p q + 4 q ^ { 2 } } { 9 p q } \times \frac { p ^ { 2 } q } { 27 p ^ { 2 } + 18 p q }$$

Evaluate

$$\frac{4q\left(3p+q\right)}{81\left(3p+2q\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{12pq+4q^{2}}{9pq}.

$$\frac{4q\left(3p+q\right)}{9pq}\times \frac{p^{2}q}{27p^{2}+18pq}$$

Cancel out q in both numerator and denominator.

$$\frac{4\left(3p+q\right)}{9p}\times \frac{p^{2}q}{27p^{2}+18pq}$$

Factor the expressions that are not already factored in \frac{p^{2}q}{27p^{2}+18pq}.

$$\frac{4\left(3p+q\right)}{9p}\times \frac{qp^{2}}{9p\left(3p+2q\right)}$$

Cancel out p in both numerator and denominator.

$$\frac{4\left(3p+q\right)}{9p}\times \frac{pq}{9\left(3p+2q\right)}$$

Multiply \frac{4\left(3p+q\right)}{9p} times \frac{pq}{9\left(3p+2q\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(3p+q\right)pq}{9p\times 9\left(3p+2q\right)}$$

Cancel out p in both numerator and denominator.

$$\frac{4q\left(3p+q\right)}{9\times 9\left(3p+2q\right)}$$

Multiply 9 and 9 to get 81.

$$\frac{4q\left(3p+q\right)}{81\left(3p+2q\right)}$$

Use the distributive property to multiply 4q by 3p+q.

$$\frac{12qp+4q^{2}}{81\left(3p+2q\right)}$$

Use the distributive property to multiply 81 by 3p+2q.

$$\frac{12qp+4q^{2}}{243p+162q}$$

Expand

$$\frac{4\left(3pq+q^{2}\right)}{81\left(3p+2q\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{12pq+4q^{2}}{9pq}.

$$\frac{4q\left(3p+q\right)}{9pq}\times \frac{p^{2}q}{27p^{2}+18pq}$$

Cancel out q in both numerator and denominator.

$$\frac{4\left(3p+q\right)}{9p}\times \frac{p^{2}q}{27p^{2}+18pq}$$

Factor the expressions that are not already factored in \frac{p^{2}q}{27p^{2}+18pq}.

$$\frac{4\left(3p+q\right)}{9p}\times \frac{qp^{2}}{9p\left(3p+2q\right)}$$

Cancel out p in both numerator and denominator.

$$\frac{4\left(3p+q\right)}{9p}\times \frac{pq}{9\left(3p+2q\right)}$$

Multiply \frac{4\left(3p+q\right)}{9p} times \frac{pq}{9\left(3p+2q\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(3p+q\right)pq}{9p\times 9\left(3p+2q\right)}$$

Cancel out p in both numerator and denominator.

$$\frac{4q\left(3p+q\right)}{9\times 9\left(3p+2q\right)}$$

Multiply 9 and 9 to get 81.

$$\frac{4q\left(3p+q\right)}{81\left(3p+2q\right)}$$

Use the distributive property to multiply 4q by 3p+q.

$$\frac{12qp+4q^{2}}{81\left(3p+2q\right)}$$

Use the distributive property to multiply 81 by 3p+2q.

$$\frac{12qp+4q^{2}}{243p+162q}$$