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\left(\sqrt{13}\right)^{2}-5\sqrt{13}-7\sqrt{13}+35
Apply the distributive property by multiplying each term of \sqrt{13}-7 by each term of \sqrt{13}-5.
13-5\sqrt{13}-7\sqrt{13}+35
The square of \sqrt{13} is 13.
13-12\sqrt{13}+35
Combine -5\sqrt{13} and -7\sqrt{13} to get -12\sqrt{13}.
48-12\sqrt{13}
Add 13 and 35 to get 48.