$$\frac { ( x + y ) ^ { 2 } } { 6 } + \frac { ( x - y ) ^ { 2 } } { 12 } - \frac { x ^ { 2 } - y ^ { 2 } } { 4 }$$
Evaluate
$\frac{y\left(x+3y\right)}{6}$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $6$ and $12$ is $12$. Multiply $\frac{\left(x+y\right)^{2}}{6}$ times $\frac{2}{2}$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $12$ and $4$ is $12$. Multiply $\frac{x^{2}-y^{2}}{4}$ times $\frac{3}{3}$.
Since $\frac{3x^{2}+3y^{2}+2xy}{12}$ and $\frac{3\left(x^{2}-y^{2}\right)}{12}$ have the same denominator, subtract them by subtracting their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $6$ and $12$ is $12$. Multiply $\frac{\left(x+y\right)^{2}}{6}$ times $\frac{2}{2}$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $12$ and $4$ is $12$. Multiply $\frac{x^{2}-y^{2}}{4}$ times $\frac{3}{3}$.
Since $\frac{3x^{2}+3y^{2}+2xy}{12}$ and $\frac{3\left(x^{2}-y^{2}\right)}{12}$ have the same denominator, subtract them by subtracting their numerators.
