Question

Which polynomial correctly combines the like terms and puts the given polynomial in standard form?

–5x3y3 + 8x4y2 – xy5 – 2x2y4 + 8x6 + 3x2y4 – 6xy5

A) –7xy5 + 5x2y4 – 5x3y3 + 8x4y2 + 8x6
B) 5xy5 + 8x4y2 + x2y4 – 5x3y3 + 8x6
C) 8x6 + 5xy5 + 8x4y2 + x2y4 – 5x3y3
D) 8x6 + 8x4y2 – 5x3y3 + x2y4 – 7xy5

Answer 1

–5x3y3 + 8x4y2 – xy5 – 2x2y4 + 8x6 + 3x2y4 – 6xy5
Answer choice:
D) 8x6 + 8x4y2 – 5x3y3 + x2y4 – 7xy5

Answer 2

Option D is correct that is
`8x^6+8x^4y^2-5x^3y^3+x^2y^4-7xy^5`

Explanation:

we have to combine the like terms

Like terms means the terms with same degree so,

for
`-5x^3y^3` has no like term since, x and y are of degree 3.

`8x^4y^2` we have no like term again since there is no other x of degree 4

`-xy^5` we have a like term
`-6xy^5`

`-2x^2y^4` we have a like term
`3x^2y^4`

`8x^6`we have no like term since, there is no other x of degree 6

Now, combining the like terms we will get

`-5x^3y^3+8x^4y^2-xy^5-6xy^5-2x^2y^4+3x^2y^4+8x^6`

After simplification we will get

`-5x^3y^3+8x^4y^2-xy^5-6xy^5-2x^2y^4+3x^2y^4+8x^6`

Rearranging the terms we will get

`8x^6+8x^4y^2-5x^3y^3+x^2y^4-7xy^5`