This question already has an answer here:
For polynomials of one variable with only and all nonzero integer coefficients, do there exist any where the polynomial consists of more than one term, and the square of the polynomial has the same number of terms or fewer than the polynomial?
For instance (to contrast), $(x + 1)^2 = x^2 + 2x + 1$
The polynomial in parentheses has two terms, but the square of the polynomial has three terms.
Another instance, $(x^2 - x + 2)^2 = x^4 - 2x^3 + 5x^2 - 4x + 4$
The polynomial in parentheses has three terms, but the square of the polynomial has five terms.
Note: This is not a duplicate of another question. That merely requested that that [p(x)]^2 had to have fewer nonzero terms than p(x). Mine requires that p(x) 1) must have all of its terms' coefficients be nonzero and integers, and 2) the number of terms could be equal, not just fewer.