Solve (m/2+4)^2+(-m/2+6)^2

$$( \frac { m } { 2 } + 4 ) ^ { 2 } + ( - \frac { m } { 2 } + 6 ) ^ { 2 }$$

Evaluate

$$\frac{m^{2}}{2}-2m+52$$

Short Solution Steps

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

$$\left(\frac{m}{2}+\frac{4\times 2}{2}\right)^{2}+\left(-\frac{m}{2}+6\right)^{2}$$

Since \frac{m}{2} and \frac{4\times 2}{2} have the same denominator, add them by adding their numerators.

$$\left(\frac{m+4\times 2}{2}\right)^{2}+\left(-\frac{m}{2}+6\right)^{2}$$

Do the multiplications in m+4\times 2.

$$\left(\frac{m+8}{2}\right)^{2}+\left(-\frac{m}{2}+6\right)^{2}$$

To raise \frac{m+8}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\left(-\frac{m}{2}+6\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{2}{2}.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\left(-\frac{m}{2}+\frac{6\times 2}{2}\right)^{2}$$

Since -\frac{m}{2} and \frac{6\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\left(\frac{-m+6\times 2}{2}\right)^{2}$$

Do the multiplications in -m+6\times 2.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\left(\frac{-m+12}{2}\right)^{2}$$

To raise \frac{-m+12}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\frac{\left(-m+12\right)^{2}}{2^{2}}$$

Since \frac{\left(m+8\right)^{2}}{2^{2}} and \frac{\left(-m+12\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(m+8\right)^{2}+\left(-m+12\right)^{2}}{2^{2}}$$

Do the multiplications in \left(m+8\right)^{2}+\left(-m+12\right)^{2}.

$$\frac{m^{2}+16m+64+m^{2}-24m+144}{2^{2}}$$

Combine like terms in m^{2}+16m+64+m^{2}-24m+144.

$$\frac{2m^{2}-8m+208}{2^{2}}$$

Factor the expressions that are not already factored in \frac{2m^{2}-8m+208}{2^{2}}.

$$\frac{2\left(m^{2}-4m+104\right)}{2^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{m^{2}-4m+104}{2}$$

Expand

$$\frac{m^{2}}{2}-2m+52$$

Short Solution Steps

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

$$\left(\frac{m}{2}+\frac{4\times 2}{2}\right)^{2}+\left(-\frac{m}{2}+6\right)^{2}$$

Since \frac{m}{2} and \frac{4\times 2}{2} have the same denominator, add them by adding their numerators.

$$\left(\frac{m+4\times 2}{2}\right)^{2}+\left(-\frac{m}{2}+6\right)^{2}$$

Do the multiplications in m+4\times 2.

$$\left(\frac{m+8}{2}\right)^{2}+\left(-\frac{m}{2}+6\right)^{2}$$

To raise \frac{m+8}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\left(-\frac{m}{2}+6\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{2}{2}.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\left(-\frac{m}{2}+\frac{6\times 2}{2}\right)^{2}$$

Since -\frac{m}{2} and \frac{6\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\left(\frac{-m+6\times 2}{2}\right)^{2}$$

Do the multiplications in -m+6\times 2.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\left(\frac{-m+12}{2}\right)^{2}$$

To raise \frac{-m+12}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(m+8\right)^{2}}{2^{2}}+\frac{\left(-m+12\right)^{2}}{2^{2}}$$

Since \frac{\left(m+8\right)^{2}}{2^{2}} and \frac{\left(-m+12\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(m+8\right)^{2}+\left(-m+12\right)^{2}}{2^{2}}$$

Do the multiplications in \left(m+8\right)^{2}+\left(-m+12\right)^{2}.

$$\frac{m^{2}+16m+64+m^{2}-24m+144}{2^{2}}$$

Combine like terms in m^{2}+16m+64+m^{2}-24m+144.

$$\frac{2m^{2}-8m+208}{2^{2}}$$

Factor the expressions that are not already factored in \frac{2m^{2}-8m+208}{2^{2}}.

$$\frac{2\left(m^{2}-4m+104\right)}{2^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{m^{2}-4m+104}{2}$$