Question

which statement is true about the polynomial $3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2$ after it has been fully simplified?

• it has 2 terms and a degree of 2.
• it has 2 terms and a degree of 3.
• it has 4 terms and a degree of 2.
• it has 4 terms and a degree of 4.

Explanation:

Step1: Combine like terms

First, identify like terms. The terms \(3x^{2}y^{2}\) and \(- 3x^{2}y^{2}\) are like terms. Combine them: \(3x^{2}y^{2}-3x^{2}y^{2}=0\). Now the polynomial simplifies to \(-5xy^{2}+2x^{2}\).

Step2: Determine number of terms and degree

• Number of terms: The simplified polynomial \(-5xy^{2}+2x^{2}\) has two terms: \(-5xy^{2}\) and \(2x^{2}\).
• Degree of a term: For a term \(ax^{m}y^{n}\), the degree is \(m + n\).
• For \(-5xy^{2}\), the degree is \(1+2 = 3\).
• For \(2x^{2}\), the degree is \(2\).
• The degree of the polynomial is the highest degree of its terms, so the degree is \(3\).

Answer:

It has 2 terms and a degree of 3.