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-why is 4x2y + 5xy classified as a 3rd degree binomial

Since both variables x^2 and y are part of the same term, we add their exponents together to determine the degree. 2+1=3, so the degree is 3.

It's a binomial because it has two terms.

To determine the correct degree and classification, see how many numbers are sectioned off by addition or subtraction signs. It could be a binomial, trinomial, or a polynomial. Once you found that, whatever the highest exponent is is the degree ( so if the highest exponent of a trinomial was 5, it would be called a fifth degree trinomial) The polynomial 4x^2y+ 5xy is a third degree binomial because there are 2 sections by one addition sign (Binomial). Then you calculate the highest exponent which is 2+1=3, so you get a third degree binomial.

Hope this helped.

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