Evaluate
2\left(p^{2}+q^{2}\right)
Expand
2p^{2}+2q^{2}
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p^{2}+2pq+q^{2}+\left(p-q\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(p+q\right)^{2}.
p^{2}+2pq+q^{2}+p^{2}-2pq+q^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(p-q\right)^{2}.
2p^{2}+2pq+q^{2}-2pq+q^{2}
Combine p^{2} and p^{2} to get 2p^{2}.
2p^{2}+q^{2}+q^{2}
Combine 2pq and -2pq to get 0.
2p^{2}+2q^{2}
Combine q^{2} and q^{2} to get 2q^{2}.
p^{2}+2pq+q^{2}+\left(p-q\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(p+q\right)^{2}.
p^{2}+2pq+q^{2}+p^{2}-2pq+q^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(p-q\right)^{2}.
2p^{2}+2pq+q^{2}-2pq+q^{2}
Combine p^{2} and p^{2} to get 2p^{2}.
2p^{2}+q^{2}+q^{2}
Combine 2pq and -2pq to get 0.
2p^{2}+2q^{2}
Combine q^{2} and q^{2} to get 2q^{2}.
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Limits
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