Solve x^2/4+3xy+9y^2

$$\frac { x ^ { 2 } } { 4 } + 3 x y + 9 y ^ { 2 }$$

Evaluate

$$\frac{\left(x+6y\right)^{2}}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3xy+9y^{2} times \frac{4}{4}.

$$\frac{x^{2}}{4}+\frac{4\left(3xy+9y^{2}\right)}{4}$$

Since \frac{x^{2}}{4} and \frac{4\left(3xy+9y^{2}\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}+4\left(3xy+9y^{2}\right)}{4}$$

Do the multiplications in x^{2}+4\left(3xy+9y^{2}\right).

$$\frac{x^{2}+12xy+36y^{2}}{4}$$

Factor

$$\frac{\left(x+6y\right)^{2}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{x^{2}+12xy+36y^{2}}{4}$$

Consider x^{2}+12xy+36y^{2}. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=x and b=6y.

$$\left(x+6y\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(x+6y\right)^{2}}{4}$$