Find a polynomial with more than one nonzero term such that its square has exactly same number of terms as the original polynomial.
Attempts-I tried to use variables for the polynomial and equate some to $0$. I also found that it is not possible for degree $1,2,3$. But I could not find a way how to find such a polynomial. Source - EJ Barbeau Polynomial.
$$\left( {x}^{4}+\sqrt{2}\; {x}^{3}-{x}^{2}+\sqrt {2}\;x+1 \right) ^{2}={x} ^{8}+2\,\sqrt {2}\;{x}^{7}+7\,{x}^{4}+2\,\sqrt {2}\;x+1 $$