Question

What is true about the completely simplified sum of the polynomials 3x^2y^2-2xy^5 and -3x^2y^2 + 3x^2y^2 + 3x^4y?

Answer 1

Given:

The polynomials are:

`3x^2y^2-2xy^5`

`-3x^2y^2+3x^2y^2+3x^4y`

To find:

The completely simplified sum of the polynomials.

Solution:

We have,

`3x^2y^2-2xy^5`

`-3x^2y^2+3x^2y^2+3x^4y`

The sum of given polynomials is:

`Sum=3x^2y^2-2xy^5-3x^2y^2+3x^2y^2+3x^4y`

`Sum=-2xy^5+3x^4y+3x^2y^2`

Therefore, the sum of the given polynomials is
`-2xy^5+3x^4y+3x^2y^2`. It is a polynomial with degree 6 and leading coefficient -2.