Which is true about the completely simplified difference of the polynomials 6x^6 − x^3 y^4 − 5x y^5 and 4x^5 y + 2x^3 y^4 + 5x y^5?

We know that it is a 7th degree polynomial with 4 terms.

In order to find this, we must first do the subtraction.

6x^6 − x^3 y^4 − 5x y^5 - (4x^5 y + 2x^3 y^4 + 5x y^5)

Then we can simplify using like terms.

6x^6 - 4x^5y - 3x^3y^4 - 10xy^5

You'll see the 4 terms in the final answer. You'll also see that the term with the highest number of variables is -3x^3y^4, which has 3 x's and 4 y's for a total of 7. This makes this a 7th degree polynomial.

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