Evaluate
16\left(\sqrt{2}x+1\right)^{2}
Expand
32x^{2}+32\sqrt{2}x+16
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16\left(\sqrt{2}\right)^{2}x^{2}+32\sqrt{2}x+16
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4\sqrt{2}x+4\right)^{2}.
16\times 2x^{2}+32\sqrt{2}x+16
The square of \sqrt{2} is 2.
32x^{2}+32\sqrt{2}x+16
Multiply 16 and 2 to get 32.
16\left(\sqrt{2}\right)^{2}x^{2}+32\sqrt{2}x+16
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4\sqrt{2}x+4\right)^{2}.
16\times 2x^{2}+32\sqrt{2}x+16
The square of \sqrt{2} is 2.
32x^{2}+32\sqrt{2}x+16
Multiply 16 and 2 to get 32.
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