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? y 3 - 6x 3 + 33x 2y + 2xy 2 + 17 20x3 - y3 + 33x 2y + 2xy 2 + 17 31x 3 - 6x 3 + 44x 2y + 11xy 2 + 17 32x 3 - y 3 + 42x 2y + 11xy 2 + 17

Answer 1

$(19x^3+44x^2y+17)-(y^3-11xy^2+2x^2y-13x^3)$
We can use the distributive property to distribute the subtraction sign:
$19x^3+44x^2y+17-y^3--11xy^2-2x^2y--13x^3$
When we subtract a negative it is the same as adding a positive:
$19x^3+44x^2y+17-y^3+11xy^2-2x^2y+13x^3$
Gather the like terms:
$19x^3+13x^3+44x^2y-2x^2y+17-y^3+11xy^2 \\ \\=32x^3+42x^2y+17-y^3+11xy^2$
Rearrange the polynomial in order of powers to x, greatest to least:
$32x^3+42x^2y+11xy^2-y^3+17$