Question

Which of the following polynomials corresponds to the subtraction of the multivariate polynomials 19x 3 + 44x 2 y + 17 and y 3 - 11xy 2 + 2x 2 y - 13x 3?

Answer 1

For this case we have the following polynomials:

$19x ^ 3 + 44x ^ 2y + 17\\y ^ 3 - 11xy ^ 2 + 2x ^ 2y - 13x ^ 3$

Subtracting both polynomials we have the following expression:

$(19x ^ 3 + 44x ^ 2y + 17) - (y ^ 3 - 11xy ^ 2 + 2x ^ 2y - 13x ^ 3)$

Grouping similar terms we have:

$x ^ 3 (19 + 13) + x ^ 2y (44 - 2) + 11xy ^ 2 - y ^ 3 + 17$

Rewriting we have:

$32x ^ 3 + 42x ^ 2y + 11xy ^ 2 - y ^ 3 + 17$

Answer:

A polynomial that corresponds to the subtraction of the multivariate polynomials is:

$32x ^ 3 + 42x ^ 2y + 11xy ^ 2 - y ^ 3 + 17$

Answer 2

The polynomial y3 - 11xy2 + 2x2y - 13x3 corresponds to the subtraction of multivariate polynomial because of the minus and plus sign in it. Also, the variables cannot be easily added or subtracted because they are all different. Unlike in the polynomial 19x3 + 44x2y + 17, it has no minus sign.