The sum of `x^4 – xy + 2y^2 and -x^4 + xy + 2y^2` is

Options

A. Monomial and polynomial in y
B. Binomial and Polynomial
C. Trinomial and polynomial
D. Monomial and polynomial in x

Answer

To find the sum of the expressions \(x^4 - xy + 2y^2\) and \(-x^4 + xy + 2y^2\), we can follow these steps:

### Step 1: Write down the expressions
We start with the two expressions:
1. \(x^4 - xy + 2y^2\)
2. \(-x^4 + xy + 2y^2\)

### Step 2: Set up the sum
We need to add these two expressions together:
\[ (x^4 - xy + 2y^2) + (-x^4 + xy + 2y^2) \]

### Step 3: Combine like terms
Now, we will combine the like terms:
- The \(x^4\) terms: \(x^4 - x^4 = 0\)
- The \(xy\) terms: \(-xy + xy = 0\)
- The \(2y^2\) terms: \(2y^2 + 2y^2 = 4y^2\)

### Step 4: Write the final result
After combining all the terms, we are left with:
\[ 0 + 0 + 4y^2 = 4y^2 \]

Thus, the sum of the two expressions is:
\[ \boxed{4y^2} \]