Solve a^2/4+a/3+1/9=

$$\frac { a ^ { 2 } } { 4 } + \frac { a } { 3 } + \frac { 1 } { 9 } =$$

Evaluate

$$\frac{\left(3a+2\right)^{2}}{36}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{a^{2}}{4} times \frac{3}{3}. Multiply \frac{a}{3} times \frac{4}{4}.

$$\frac{3a^{2}}{12}+\frac{4a}{12}+\frac{1}{9}$$

Since \frac{3a^{2}}{12} and \frac{4a}{12} have the same denominator, add them by adding their numerators.

$$\frac{3a^{2}+4a}{12}+\frac{1}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 9 is 36. Multiply \frac{3a^{2}+4a}{12} times \frac{3}{3}. Multiply \frac{1}{9} times \frac{4}{4}.

$$\frac{3\left(3a^{2}+4a\right)}{36}+\frac{4}{36}$$

Since \frac{3\left(3a^{2}+4a\right)}{36} and \frac{4}{36} have the same denominator, add them by adding their numerators.

$$\frac{3\left(3a^{2}+4a\right)+4}{36}$$

Do the multiplications in 3\left(3a^{2}+4a\right)+4.

$$\frac{9a^{2}+12a+4}{36}$$

Factor

$$\frac{\left(3a+2\right)^{2}}{36}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{9a^{2}+12a+4}{36}$$

Consider 9a^{2}+12a+4. Use the perfect square formula, p^{2}+2pq+q^{2}=\left(p+q\right)^{2}, where p=3a and q=2.

$$\left(3a+2\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(3a+2\right)^{2}}{36}$$