Question

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

• the sum is a trinomial with a degree of 5.
• the sum is a trinomial with a degree of 6.
• the sum is a binomial with a degree of 5.
• the sum is a binomial with a degree of 6.

Explanation:

Step1: Write the sum of polynomials

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

Step2: Combine like terms

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

Step3: Determine type and degree

Count terms: 2 (binomial). Calculate term degrees:
For $-2xy^5$: $1+5=6$; For $3x^4y$: $4+1=5$. Highest degree is 6.

Answer:

The sum is a binomial with a degree of 6.