Evaluate
\left(x+y\right)^{2}+\left(x-3y\right)^{2}
Expand
2x^{2}-4xy+10y^{2}
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x^{2}+2xy+y^{2}+\left(x-3y\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.
x^{2}+2xy+y^{2}+x^{2}-6xy+9y^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3y\right)^{2}.
2x^{2}+2xy+y^{2}-6xy+9y^{2}
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}-4xy+y^{2}+9y^{2}
Combine 2xy and -6xy to get -4xy.
2x^{2}-4xy+10y^{2}
Combine y^{2} and 9y^{2} to get 10y^{2}.
x^{2}+2xy+y^{2}+\left(x-3y\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.
x^{2}+2xy+y^{2}+x^{2}-6xy+9y^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3y\right)^{2}.
2x^{2}+2xy+y^{2}-6xy+9y^{2}
Combine x^{2} and x^{2} to get 2x^{2}.
2x^{2}-4xy+y^{2}+9y^{2}
Combine 2xy and -6xy to get -4xy.
2x^{2}-4xy+10y^{2}
Combine y^{2} and 9y^{2} to get 10y^{2}.
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