Solve m^2+2m+2/2*1/2m^2+m-4

$$\frac { m ^ { 2 } + 2 m + 2 } { 2 } \times \frac { 1 } { 2 } m ^ { 2 } + m - 4$$

Evaluate

$$\frac{m^{4}}{4}+\frac{m^{3}}{2}+\frac{m^{2}}{2}+m-4$$

Short Solution Steps

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

$$\frac{m^{2}+2m+2}{2\times 2}m^{2}+m-4$$

Express \frac{m^{2}+2m+2}{2\times 2}m^{2} as a single fraction.

$$\frac{\left(m^{2}+2m+2\right)m^{2}}{2\times 2}+m-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply m-4 times \frac{2\times 2}{2\times 2}.

$$\frac{\left(m^{2}+2m+2\right)m^{2}}{2\times 2}+\frac{\left(m-4\right)\times 2\times 2}{2\times 2}$$

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

$$\frac{\left(m^{2}+2m+2\right)m^{2}+\left(m-4\right)\times 2\times 2}{2\times 2}$$

Do the multiplications in \left(m^{2}+2m+2\right)m^{2}+\left(m-4\right)\times 2\times 2.

$$\frac{m^{4}+2m^{3}+2m^{2}+4m-16}{2\times 2}$$

Expand 2\times 2.

$$\frac{m^{4}+2m^{3}+2m^{2}+4m-16}{4}$$

Expand

$$\frac{m^{4}}{4}+\frac{m^{3}}{2}+\frac{m^{2}}{2}+m-4$$

Short Solution Steps

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

$$\frac{m^{2}+2m+2}{2\times 2}m^{2}+m-4$$

Express \frac{m^{2}+2m+2}{2\times 2}m^{2} as a single fraction.

$$\frac{\left(m^{2}+2m+2\right)m^{2}}{2\times 2}+m-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply m-4 times \frac{2\times 2}{2\times 2}.

$$\frac{\left(m^{2}+2m+2\right)m^{2}}{2\times 2}+\frac{\left(m-4\right)\times 2\times 2}{2\times 2}$$

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

$$\frac{\left(m^{2}+2m+2\right)m^{2}+\left(m-4\right)\times 2\times 2}{2\times 2}$$

Do the multiplications in \left(m^{2}+2m+2\right)m^{2}+\left(m-4\right)\times 2\times 2.

$$\frac{m^{4}+2m^{3}+2m^{2}+4m-16}{2\times 2}$$

Expand 2\times 2.

$$\frac{m^{4}+2m^{3}+2m^{2}+4m-16}{4}$$