[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
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\\=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]
