Polynomial not sum of squares

Let $P(x,y) = x^2y^4 + x^4y^2 + 1 - 3x^2y^2$

a.) Prove that $P(x,y)$ is non-negative

b.) Prove that $P(x,y)$ cannot be expressed as a sum of squares of polynomials.

n-expressible integers

A positive integer is called $n$-expressible if it can be written as a sum of $n$ or less squares.

Prove that the product of two $n$-expressible integers is $\frac{n^2-n+2}{2}$-expressible