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