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\left(\sqrt{19}\right)^{2}-1^{2}+\left(1+\sqrt{10}\right)\left(\sqrt{10}-1\right)
Consider \left(\sqrt{19}+1\right)\left(\sqrt{19}-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
19-1^{2}+\left(1+\sqrt{10}\right)\left(\sqrt{10}-1\right)
The square of \sqrt{19} is 19.
19-1+\left(1+\sqrt{10}\right)\left(\sqrt{10}-1\right)
Calculate 1 to the power of 2 and get 1.
18+\left(1+\sqrt{10}\right)\left(\sqrt{10}-1\right)
Subtract 1 from 19 to get 18.
18+\sqrt{10}-1+\left(\sqrt{10}\right)^{2}-\sqrt{10}
Apply the distributive property by multiplying each term of 1+\sqrt{10} by each term of \sqrt{10}-1.
18+\sqrt{10}-1+10-\sqrt{10}
The square of \sqrt{10} is 10.
18+\sqrt{10}+9-\sqrt{10}
Add -1 and 10 to get 9.
18+9
Combine \sqrt{10} and -\sqrt{10} to get 0.
27
Add 18 and 9 to get 27.