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The polynomial correctly combines the like terms and puts the given polynomial in standard form is [tex]\rm 8x^6+ 8x^4y^2 - 5x^3y^3 +x^2y^4 -7xy^5.[/tex]
The correct option is D.
Given
Expression; [tex]\rm -5x3y^3 + 8x4y^2 - xy^5 - 2x2y^4 + 8x^6 + 3x^2y^4 - 6xy^5[/tex]
A polynomial is an expression consisting of coefficients and variables which are also known as indeterminates.
We have to combine the like terms which means the terms with the same degree.
Therefore,
The correctly combines the like terms;
[tex]\rm =-5x^3y^3 + 8x^4y^2 - xy^5 - 2x^2y^4 + 8x^6 + 3x^2y^4 - 6xy^5\\\\=8x^6 +8x^4y^2--5x^3y^3+ 3x^2y^4- 2x^2y^4 - xy^5 -6xy^5\\\\= 8x^6+ 8x^4y^2 - 5x^3y^3 +x^2y^4 -7xy^5.[/tex]
Hence, the polynomial correctly combines the like terms and puts the given polynomial in standard form is [tex]\rm 8x^6+ 8x^4y^2 - 5x^3y^3 +x^2y^4 -7xy^5.[/tex]
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