In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^4 y^2−5x^2 y^2+3xy)+(−18x^4 y^2−6x^2 y^2−xy)

Key Concepts

Polynomial Operations

Polynomial operations involve adding, subtracting, and multiplying polynomials. When adding or subtracting polynomials, like terms (terms with the same variable and exponent) are combined. This process is essential for simplifying expressions and determining the resulting polynomial's degree.

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 shape. For example, in the polynomial 7x^4y^2, the degree is 4, as it is the highest exponent of x present in the terms.

Like Terms

Like terms are terms in a polynomial that have the same variable raised to the same power. Identifying like terms is crucial for performing operations such as addition and subtraction. For instance, in the expression 7x^4y^2 and -18x^4y^2, both terms are like terms and can be combined.