Perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^2-8xy+y^2)+(-8x^2-9xy-4y^2)

Verified step by step guidance

1. Combine like terms: Start by grouping the terms with the same variables together.
2. Add the coefficients of the like terms: For the x^2 terms, add 7 and -8. For the xy terms, add -8 and -9. For the y^2 terms, add 1 and -4.
3. Write the resulting polynomial after combining the like terms.
4. Identify the degree of the polynomial: The degree is the highest sum of the exponents of the variables in any single term.
5. State the degree of the resulting polynomial.

Key Concepts

Polynomial Operations

Polynomial operations involve adding, subtracting, multiplying, or dividing polynomial expressions. In this case, we are focusing on addition, which requires combining like terms—terms that have the same variable raised to the same power. Understanding how to identify and combine these terms is essential for simplifying the expression correctly.

Like Terms

Like terms are terms in a polynomial that share the same variable and exponent. For example, in the expression 7x^2 and -8x^2, both terms are like terms because they both contain the variable x raised to the power of 2. Recognizing and grouping like terms is crucial for performing polynomial addition accurately.

Degree of a Polynomial

The degree of a polynomial is the highest power of the variable in the expression. It provides insight into the polynomial's behavior and characteristics. After performing the indicated operations, determining the degree involves identifying the term with the largest exponent in the resulting polynomial, which is important for understanding its overall structure.