Question

Which polynomial correctly combines the like terms and puts the given polynomial in standard form? -5x^3y^3+8x^4y^2-xy^5-2x^2y^4+8x^6+3x^2y^4-6xy^5

Answer 1

Given:

The polynomial is:

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

To find:

The simplified form of the given polynomial in standard form.

Solution:

We have,

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

Combining the like terms, we get

$=-5x^3y^3+8x^4y^2+(-2x^2y^4+3x^2y^4)+8x^6+(-xy^5-6xy^5)$

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

Now, rewrite this polynomial in standard form.

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

Therefore, the required polynomial in standard form is $8x^6+8x^4y^2-5x^3y^3+x^2y^4-7xy^5$.