Solve (p-q)(p+4q)+4q^2/3p+qq

$$\frac { ( p - q ) ( p + 4 q ) + 4 q ^ { 2 } } { 3 p + q q }$$

Evaluate

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

Short Solution Steps

Multiply q and q to get q^{2}.

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

Use the distributive property to multiply p-q by p+4q and combine like terms.

$$\frac{p^{2}+3pq-4q^{2}+4q^{2}}{3p+q^{2}}$$

Combine -4q^{2} and 4q^{2} to get 0.

$$\frac{p^{2}+3pq}{3p+q^{2}}$$

Expand

$$\frac{p^{2}+3pq}{3p+q^{2}}$$

Short Solution Steps

Multiply q and q to get q^{2}.

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

Use the distributive property to multiply p-q by p+4q and combine like terms.

$$\frac{p^{2}+3pq-4q^{2}+4q^{2}}{3p+q^{2}}$$

Combine -4q^{2} and 4q^{2} to get 0.

$$\frac{p^{2}+3pq}{3p+q^{2}}$$