What polynomials corresponds to the subtraction of the multivariate polynomials 19x 3 plus 44x 2 y plus 17 and y 3 - 11xy 2 plus 2x13x 3?

Answer 1

To subtract the multivariate polynomials (19x^3 + 44x^2y + 17) and (y^3 - 11xy^2 + 2x + 13x^3), we first rewrite the second polynomial with a negative sign: (- (y^3 - 11xy^2 + 2x + 13x^3)). Combining the polynomials gives us:

[ (19x^3 - 13x^3) + 44x^2y + 17 - y^3 + 11xy^2 - 2x. ]

This simplifies to:

[ 6x^3 + 44x^2y + 11xy^2 - y^3 - 2x + 17. ]

Thus, the resulting polynomial after subtraction is (6x^3 + 44x^2y + 11xy^2 - y^3 - 2x + 17).