Solve 1/2p-(p+2)^2-q/6p^2

$$\frac { 1 } { 2 p } - \frac { ( p + 2 ) ^ { 2 } - q } { 6 p ^ { 2 } }$$

Evaluate

$$\frac{-p^{2}-p+q-4}{6p^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2p and 6p^{2} is 6p^{2}. Multiply \frac{1}{2p} times \frac{3p}{3p}.

$$\frac{3p}{6p^{2}}-\frac{\left(p+2\right)^{2}-q}{6p^{2}}$$

Since \frac{3p}{6p^{2}} and \frac{\left(p+2\right)^{2}-q}{6p^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3p-\left(\left(p+2\right)^{2}-q\right)}{6p^{2}}$$

Do the multiplications in 3p-\left(\left(p+2\right)^{2}-q\right).

$$\frac{3p-p^{2}-4p-4+q}{6p^{2}}$$

Combine like terms in 3p-p^{2}-4p-4+q.

$$\frac{-p-p^{2}-4+q}{6p^{2}}$$

Expand

$$\frac{-p^{2}-p+q-4}{6p^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2p and 6p^{2} is 6p^{2}. Multiply \frac{1}{2p} times \frac{3p}{3p}.

$$\frac{3p}{6p^{2}}-\frac{\left(p+2\right)^{2}-q}{6p^{2}}$$

Since \frac{3p}{6p^{2}} and \frac{\left(p+2\right)^{2}-q}{6p^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3p-\left(\left(p+2\right)^{2}-q\right)}{6p^{2}}$$

Do the multiplications in 3p-\left(\left(p+2\right)^{2}-q\right).

$$\frac{3p-p^{2}-4p-4+q}{6p^{2}}$$

Combine like terms in 3p-p^{2}-4p-4+q.

$$\frac{-p-p^{2}-4+q}{6p^{2}}$$