Solve p_{1}(frac{2-p_{1}}{2})+[p/2(1/2)(1/2)]

$$p _ { 1 } ( \frac { 2 - p _ { 1 } } { 2 } ) + [ \frac { p } { 2 } ( \frac { 1 } { 2 } ) ( \frac { 1 } { 2 } ) ]$$

Evaluate

$$-\frac{p_{1}^{2}}{2}+\frac{p}{8}+p_{1}$$

Short Solution Steps

Express p_{1}\times \frac{2-p_{1}}{2} as a single fraction.

$$\frac{p_{1}\left(2-p_{1}\right)}{2}+\frac{p}{2}\times \frac{1}{2}\times \frac{1}{2}$$

Multiply \frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{p_{1}\left(2-p_{1}\right)}{2}+\frac{p}{2}\times \frac{1\times 1}{2\times 2}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$\frac{p_{1}\left(2-p_{1}\right)}{2}+\frac{p}{2}\times \frac{1}{4}$$

Multiply \frac{p}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{p_{1}\left(2-p_{1}\right)}{2}+\frac{p}{2\times 4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2\times 4 is 2\times 4. Multiply \frac{p_{1}\left(2-p_{1}\right)}{2} times \frac{4}{4}.

$$\frac{4p_{1}\left(2-p_{1}\right)}{2\times 4}+\frac{p}{2\times 4}$$

Since \frac{4p_{1}\left(2-p_{1}\right)}{2\times 4} and \frac{p}{2\times 4} have the same denominator, add them by adding their numerators.

$$\frac{4p_{1}\left(2-p_{1}\right)+p}{2\times 4}$$

Do the multiplications in 4p_{1}\left(2-p_{1}\right)+p.

$$\frac{8p_{1}-4p_{1}^{2}+p}{2\times 4}$$

Expand 2\times 4.

$$\frac{8p_{1}-4p_{1}^{2}+p}{8}$$

Expand

$$-\frac{p_{1}^{2}}{2}+\frac{p}{8}+p_{1}$$

Short Solution Steps

Express p_{1}\times \frac{2-p_{1}}{2} as a single fraction.

$$\frac{p_{1}\left(2-p_{1}\right)}{2}+\frac{p}{2}\times \frac{1}{2}\times \frac{1}{2}$$

Multiply \frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{p_{1}\left(2-p_{1}\right)}{2}+\frac{p}{2}\times \frac{1\times 1}{2\times 2}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$\frac{p_{1}\left(2-p_{1}\right)}{2}+\frac{p}{2}\times \frac{1}{4}$$

Multiply \frac{p}{2} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{p_{1}\left(2-p_{1}\right)}{2}+\frac{p}{2\times 4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2\times 4 is 2\times 4. Multiply \frac{p_{1}\left(2-p_{1}\right)}{2} times \frac{4}{4}.

$$\frac{4p_{1}\left(2-p_{1}\right)}{2\times 4}+\frac{p}{2\times 4}$$

Since \frac{4p_{1}\left(2-p_{1}\right)}{2\times 4} and \frac{p}{2\times 4} have the same denominator, add them by adding their numerators.

$$\frac{4p_{1}\left(2-p_{1}\right)+p}{2\times 4}$$

Do the multiplications in 4p_{1}\left(2-p_{1}\right)+p.

$$\frac{8p_{1}-4p_{1}^{2}+p}{2\times 4}$$

Expand 2\times 4.

$$\frac{8p_{1}-4p_{1}^{2}+p}{8}$$