Solve [(3m+4n)+(2m+5n]*(m+2n)div2

$$[ ( 3 m + 4 n ) + ( 2 m + 5 n ] \times ( m + 2 n ) \div 2$$

Evaluate

$$\frac{\left(m+2n\right)\left(2m+5n\right)+6m+8n}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3m+4n times \frac{2}{2}.

$$\frac{2\left(3m+4n\right)}{2}+\frac{\left(2m+5n\right)\left(m+2n\right)}{2}$$

Since \frac{2\left(3m+4n\right)}{2} and \frac{\left(2m+5n\right)\left(m+2n\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(3m+4n\right)+\left(2m+5n\right)\left(m+2n\right)}{2}$$

Do the multiplications in 2\left(3m+4n\right)+\left(2m+5n\right)\left(m+2n\right).

$$\frac{6m+8n+2m^{2}+4mn+5nm+10n^{2}}{2}$$

Combine like terms in 6m+8n+2m^{2}+4mn+5nm+10n^{2}.

$$\frac{6m+8n+2m^{2}+10n^{2}+9mn}{2}$$

Expand

$$\frac{9mn}{2}+5n^{2}+m^{2}+3m+4n$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3m+4n times \frac{2}{2}.

$$\frac{2\left(3m+4n\right)}{2}+\frac{\left(2m+5n\right)\left(m+2n\right)}{2}$$

Since \frac{2\left(3m+4n\right)}{2} and \frac{\left(2m+5n\right)\left(m+2n\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(3m+4n\right)+\left(2m+5n\right)\left(m+2n\right)}{2}$$

Do the multiplications in 2\left(3m+4n\right)+\left(2m+5n\right)\left(m+2n\right).

$$\frac{6m+8n+2m^{2}+4mn+5nm+10n^{2}}{2}$$

Combine like terms in 6m+8n+2m^{2}+4mn+5nm+10n^{2}.

$$\frac{6m+8n+2m^{2}+10n^{2}+9mn}{2}$$