The polynomial that correctly combines the like terms and to express in standard form is Option (D) [tex]3x^{4} + x^{3}y - 8x^{2}y^{2} + 9xy^{3} - 13y^{4}[/tex] .
Given polynomial is -
= [tex]9xy^{3} - 4y^{4} -10x^{2}y^{2} + x^{3}y + 3x^{4} + 2x^{2}y^{2} - 9y^{4}[/tex]
Separating the like terms from the above polynomial -
= [tex]9xy^{3} + (-10x^{2}y^{2} + 2x^{2}y^{2})+ x^{3}y + 3x^{4}+( - 9y^{4} - 4y^{4})[/tex]
Expressing the polynomial in standard form -
= [tex]3x^{4} + x^{3}y - 8x^{2}y^{2} + 9xy^{3} - 13y^{4}[/tex]
Therefore the polynomial that correctly combines the like terms and to express in standard form is Option (D) [tex]3x^{4} + x^{3}y - 8x^{2}y^{2} + 9xy^{3} - 13y^{4}[/tex] .
To learn more about solving polynomial expression, refer -
https://brainly.com/question/12240569
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