Question: How do I extract terms from multivariate polynomials?

Hello everyone. I want to know how I can extract terms with the lowest sum of the degree of x and of y in a multivariate polynomial (in x and y)?

For instance, if I've f(x) = 100x^2y^2 + 35x^2y + 45y, I want an output of 45y.

On the other hand, if I've g(x) = 13x^2y^2 + xy^2 + 2yx^2, I want an output of xy^2 + yx^2.

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