Question 350123
First,
{{{(a+4)^2}}} does not equal {{{a^2+4^2}}}.
Using the FOIL method,
{{{(a+4)^2=(a+4)(a+4)}}}
{{{(a+4)^2=a^2+4a+4a+4^2}}}
{{{(a+4)^2=a^2+8a+4^2}}}
There is a cross product term.
As an example,
{{{(1+2)^2=3^2=9}}}
If we did it like you showed,
{{{(1+2)^2=1+4=5 }}}
which is clearly incorrect.
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The answer is {{{(a+4)}}} but that may not be the complete answer because {{{-(a+4)}}} is also an answer since {{{-(a+4)*(-(a+4))=(a+4)^2}}}