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\frac{1}{4}\left(x^{2}+8x+16\right)+3
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.
\frac{1}{4}x^{2}+2x+4+3
Use the distributive property to multiply \frac{1}{4} by x^{2}+8x+16.
\frac{1}{4}x^{2}+2x+7
Add 4 and 3 to get 7.
\frac{1}{4}\left(x^{2}+8x+16\right)+3
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.
\frac{1}{4}x^{2}+2x+4+3
Use the distributive property to multiply \frac{1}{4} by x^{2}+8x+16.
\frac{1}{4}x^{2}+2x+7
Add 4 and 3 to get 7.