Evaluate
\frac{\left(x+y\right)^{2}}{4}
Expand
\frac{xy}{2}+\frac{x^{2}}{4}+\frac{y^{2}}{4}
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\left(\frac{1}{2}x+\frac{1}{2}y\right)^{2}
Use the distributive property to multiply \frac{1}{2} by x+y.
\frac{1}{4}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{2}x+\frac{1}{2}y\right)^{2}.
\left(\frac{1}{2}x+\frac{1}{2}y\right)^{2}
Use the distributive property to multiply \frac{1}{2} by x+y.
\frac{1}{4}x^{2}+\frac{1}{2}xy+\frac{1}{4}y^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{1}{2}x+\frac{1}{2}y\right)^{2}.
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