Simplify \(\sqrt{28}\) to \(2\sqrt{7}\).
\[{(6-\sqrt{7})}^{2}+{(3+\sqrt{7})}^{2}-3(1-2\sqrt{7}).\]
Use Square of Difference: \({(a-b)}^{2}={a}^{2}-2ab+{b}^{2}\).
\[{6}^{2}-2\times 6\sqrt{7}+{\sqrt{7}}^{2}+{(3+\sqrt{7})}^{2}-3(1-2\sqrt{7}).\]
Use Square of Sum: \({(a+b)}^{2}={a}^{2}+2ab+{b}^{2}\).
\[{6}^{2}-2\times 6\sqrt{7}+{\sqrt{7}}^{2}+{3}^{2}+2\times 3\sqrt{7}+{\sqrt{7}}^{2}-3(1-2\sqrt{7}).\]
Simplify \({6}^{2}\) to \(36\).
\[36-2\times 6\sqrt{7}+{\sqrt{7}}^{2}+{3}^{2}+2\times 3\sqrt{7}+{\sqrt{7}}^{2}-3(1-2\sqrt{7}).\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[36-2\times 6\sqrt{7}+7+{3}^{2}+2\times 3\sqrt{7}+7-3(1-2\sqrt{7}).\]
Simplify \({3}^{2}\) to \(9\).
\[36-2\times 6\sqrt{7}+7+9+2\times 3\sqrt{7}+7-3(1-2\sqrt{7}).\]
Simplify \(2\times 6\sqrt{7}\) to \(12\sqrt{7}\).
\[36-12\sqrt{7}+7+9+2\times 3\sqrt{7}+7-3(1-2\sqrt{7}).\]
Simplify \(2\times 3\sqrt{7}\) to \(6\sqrt{7}\).
\[36-12\sqrt{7}+7+9+6\sqrt{7}+7-3(1-2\sqrt{7}).\]
Collect like terms.
\[(36+7+9+7)+(-12\sqrt{7}+6\sqrt{7})-3(1-2\sqrt{7}).\]
Simplify.
\[59-6\sqrt{7}-3(1-2\sqrt{7}).\]
59-6*sqrt(7)-3*(1-2*sqrt(7)).
