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<p>Consider the polynomial p(x,y)=x4+y4+x2+y2. Express p(x,y) as the sum of squares of three polynomials over R in x and y .</p>
<p>https://math.stackexchange.com/questions/248487/find-three-polynomials-whose-squares-sum-up-to-x4-y4-x2-y2 here is a link with the soln...hope it helps</p>