To determine the correct statement about the polynomial [tex]\( 3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2 \)[/tex] after it has been fully simplified, let's proceed step-by-step with the simplification process.
### Step-by-Step Simplification:
1. Write down the polynomial:
[tex]\[ 3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2 \][/tex]
2. Combine like terms:
- Notice that [tex]\( 3x^2y^2 \)[/tex] and [tex]\( -3x^2y^2 \)[/tex] are like terms and can be combined:
[tex]\[ 3x^2y^2 - 3x^2y^2 = 0 \][/tex]
- After combining these terms, the polynomial simplifies to:
[tex]\[ 0 - 5xy^2 + 2x^2 \][/tex]
Which is:
[tex]\[ -5xy^2 + 2x^2 \][/tex]
3. Count the remaining terms:
- The simplified polynomial [tex]\( -5xy^2 + 2x^2 \)[/tex] consists of 2 terms: [tex]\( -5xy^2 \)[/tex] and [tex]\( 2x^2 \)[/tex].
4. Determine the degree of the polynomial:
- The degree of a term in a polynomial is the sum of the exponents of the variables in that term.
- For the term [tex]\( -5xy^2 \)[/tex]:
- The degree is [tex]\( 1 \)[/tex] (from [tex]\( x \)[/tex]) + [tex]\( 2 \)[/tex] (from [tex]\( y^2 \)[/tex]) = [tex]\( 3 \)[/tex].
- For the term [tex]\( 2x^2 \)[/tex]:
- The degree is [tex]\( 2 \)[/tex] (from [tex]\( x^2 \)[/tex]).
- The degree of the polynomial is the highest degree of its terms, which in this case is [tex]\( 3 \)[/tex] (from [tex]\( -5xy^2 \)[/tex]).
### Conclusion:
After fully simplifying the polynomial [tex]\( 3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2 \)[/tex], we have:
- 2 terms: [tex]\( -5xy^2 \)[/tex] and [tex]\( 2x^2 \)[/tex].
- The highest degree term has a degree of [tex]\( 3 \)[/tex].
Therefore, the correct statement is:
It has 2 terms and a degree of 3.
