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