If (f(x)=x^2+2) and (g(x)=4x), how can ((f+g)(x)) be written in complete square form?

Correct answer: ((x+2)^2-2)

The direct answer is option A, \\(x+2)^2-2\\). First add the functions: \\( (f+g)(x)=f(x)+g(x)=(x^2+2)+4x=x^2+4x+2\\). To complete the square, take half of the coefficient of x, namely 4 divided by 2, which is 2. Add and subtract its square, 4: \\(x^2+4x+2=x^2+4x+4-4+2=(x+2)^2-2\\). Thus option A is correct. Option B gives \\(x^2-4x+2\\), so its middle term has the wrong sign. Option C expands to \\(x^2+4x+6\\), not the required expression. Option D expands to \\(x^2-8x+18\\), so both the middle term and constant are wrong. The safe method is: half the x-coefficient, square it, add and subtract that square.