which polynomial correctly combines the like terms and puts the given polynomial in standard form…

which polynomial correctly combines the like terms and puts the given polynomial in standard form? -5x^{3}y^{3}+8x^{4}y^{2}-xy^{5}-2x^{2}y^{4}+8x^{6}+3x^{2}y^{4}-6xy^{5}\n-7xy^{5}+5x^{2}y^{4}-5x^{3}y^{3}+8x^{4}y^{2}+8x^{6}\n5xy^{5}+8x^{4}y^{2}+x^{2}y^{4}-5x^{3}y^{3}+8x^{6}\n8x^{6}+5xy^{5}+8x^{4}y^{2}+x^{2}y^{4}-5x^{3}y^{3}\n8x^{6}+8x^{4}y^{2}-5x^{3}y^{3}+x^{2}y^{4}-7xy^{5}

which polynomial correctly combines the like terms and puts the given polynomial in standard form? -5x^{3}y^{3}+8x^{4}y^{2}-xy^{5}-2x^{2}y^{4}+8x^{6}+3x^{2}y^{4}-6xy^{5}\n-7xy^{5}+5x^{2}y^{4}-5x^{3}y^{3}+8x^{4}y^{2}+8x^{6}\n5xy^{5}+8x^{4}y^{2}+x^{2}y^{4}-5x^{3}y^{3}+8x^{6}\n8x^{6}+5xy^{5}+8x^{4}y^{2}+x^{2}y^{4}-5x^{3}y^{3}\n8x^{6}+8x^{4}y^{2}-5x^{3}y^{3}+x^{2}y^{4}-7xy^{5}

Answer

Explanation:

Step1: Combine like - terms

The terms with (xy^{5}) are (-xy^{5}-6xy^{5}=-7xy^{5}). The terms with (x^{2}y^{4}) are (- 2x^{2}y^{4}+3x^{2}y^{4}=x^{2}y^{4}). The other terms (-5x^{3}y^{3}), (8x^{4}y^{2}), (8x^{6}) remain as they are since there are no like - terms for them in the given polynomial.

Step2: Write in standard form

In a polynomial in two variables (x) and (y), the standard form is written in descending order of the sum of the exponents of (x) and (y) for each term. The sum of exponents for (8x^{6}) is 6, for (8x^{4}y^{2}) is (4 + 2=6), for (-5x^{3}y^{3}) is (3+3 = 6), for (x^{2}y^{4}) is (2 + 4=6) and for (-7xy^{5}) is (1+5 = 6). We order them alphabetically by (x) (when the sum of exponents is the same). So the polynomial in standard form is (8x^{6}+8x^{4}y^{2}-5x^{3}y^{3}+x^{2}y^{4}-7xy^{5}).

Answer:

D. (8x^{6}+8x^{4}y^{2}-5x^{3}y^{3}+x^{2}y^{4}-7xy^{5})