Question 495911
These aren't equal because you can't distribute an exponent.  When you raise something to the second power (square it), you're multiplying it by itself; thus, {{{(x+4)^2}}} means {{{(x+4)(x+4)}}}.  If you use FOIL to multiply, you get {{{x^2 + 4x+ 4x + 16}}}, or {{{x^2+8x+16}}}.  When you just distribute the exponent, you lose that middle "+8x" term, which is why {{{(x+4)^2}}} and {{{x^2+16}}} are not equal.


I'm not sure what you mean about the solution to {{{x^2+16}}}.  That is already simplified; it's just not the same as {{{(x+4)^2}}}, which is {{{x^2+8x+16}}}.