Question

what constant must be added to x^4+8^2+ to make it perfect square trinomial ?

Answer 1

Is that supposed to be \[x^4+8x^2\]?

a perfect square is of the form
\[(u+a)^2 = u^2 + 2au + a^2\]If we compare that with yours:
\[x^4+8x^2\]\[u^2+2au + a^2\]
\[x^4=u^2\]\[x^2=u\]
\[8x^2 = 2au\]\[8=2a\]\[4=a\]

So we need to add what to our expression to make it a perfect square?

Answer 2

[x^2 + 4]^2 = x^4 + 8x^2 + 16
Answer: Add 16