Question

Which of the following polynomials corresponds to the subtraction of the multivariate polynomials 19x^3+44x^2y+17 and y^3-11xy^2+2x^2y-13x^3
A. y^3-6x^3+33x^2y+2x^2y+17

B. 20x^3-y^3+33x^2y+2x^2y+17

C. 31x^3-6x^3+44x^2y+11x^2y+17

D. 32x^3-y^3+42x^2y+11x^2y+17

Answer 1

Name the two given polynomials as
f(x) = 19x³ + 44x²y + 17
g(x) = y³ - 11xy² + 2x²y - 13x³

Create the subtraction f(x) - g(x).
f(x)-g(x) = 19x³ + 44x²y + 17 - (y³ - 11xy² + 2x²y - 13x³)
             = (19 + 13)x³ + (44 - 2)x²y + 11xy² - y³ + 17
             = 32x³ - y³ + 42x²y + 11xy² + 17

Answer: D
Note that answer D has a typo. 11xy² is correct, but 11x²y is not.