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3\left(\left(\sqrt{2}\right)^{2}-4\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{2}-2\sqrt{3}\right)^{2}.
3\left(2-4\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}\right)
The square of \sqrt{2} is 2.
3\left(2-4\sqrt{6}+4\left(\sqrt{3}\right)^{2}\right)
To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.
3\left(2-4\sqrt{6}+4\times 3\right)
The square of \sqrt{3} is 3.
3\left(2-4\sqrt{6}+12\right)
Multiply 4 and 3 to get 12.
3\left(14-4\sqrt{6}\right)
Add 2 and 12 to get 14.
42-12\sqrt{6}
Use the distributive property to multiply 3 by 14-4\sqrt{6}.
3\left(\left(\sqrt{2}\right)^{2}-4\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{2}-2\sqrt{3}\right)^{2}.
3\left(2-4\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}\right)
The square of \sqrt{2} is 2.
3\left(2-4\sqrt{6}+4\left(\sqrt{3}\right)^{2}\right)
To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.
3\left(2-4\sqrt{6}+4\times 3\right)
The square of \sqrt{3} is 3.
3\left(2-4\sqrt{6}+12\right)
Multiply 4 and 3 to get 12.
3\left(14-4\sqrt{6}\right)
Add 2 and 12 to get 14.
42-12\sqrt{6}
Use the distributive property to multiply 3 by 14-4\sqrt{6}.