Solve n^2/9+2mn+9m^2

$$\frac { n ^ { 2 } } { 9 } + 2 m n + 9 m ^ { 2 }$$

Evaluate

$$\frac{\left(9m+n\right)^{2}}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2mn+9m^{2} times \frac{9}{9}.

$$\frac{n^{2}}{9}+\frac{9\left(2mn+9m^{2}\right)}{9}$$

Since \frac{n^{2}}{9} and \frac{9\left(2mn+9m^{2}\right)}{9} have the same denominator, add them by adding their numerators.

$$\frac{n^{2}+9\left(2mn+9m^{2}\right)}{9}$$

Do the multiplications in n^{2}+9\left(2mn+9m^{2}\right).

$$\frac{n^{2}+18mn+81m^{2}}{9}$$

Factor

$$\frac{\left(9m+n\right)^{2}}{9}$$

Solution Steps

Factor out \frac{1}{9}.

$$\frac{n^{2}+18mn+81m^{2}}{9}$$

Consider n^{2}+18mn+81m^{2}. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=9m and b=n.

$$\left(9m+n\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(9m+n\right)^{2}}{9}$$