In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers.(7x²y − 5xy) + (2x²y − xy)

Verified step by step guidance

1. Identify the like terms in the polynomials: terms with the same variables raised to the same powers.
2. The first polynomial is \(7x^2y - 5xy\) and the second polynomial is \(2x^2y - xy\).
3. Combine the like terms: \(7x^2y\) and \(2x^2y\) are like terms, and \(-5xy\) and \(-xy\) are like terms.
4. Add the coefficients of the like terms: \(7x^2y + 2x^2y\) and \(-5xy - xy\).
5. Write the resulting polynomial by combining the sums of the like terms.

Key Concepts

Polynomials

Polynomials are algebraic expressions that consist of variables raised to whole number exponents and coefficients. They can include terms like constants, linear terms, quadratic terms, and higher degrees. Understanding the structure of polynomials is essential for performing operations such as addition, subtraction, and multiplication.

Like Terms

Like terms are terms in a polynomial that have the same variable parts raised to the same powers. For example, in the expression 3x² and 5x², both terms are like terms because they share the same variable x raised to the power of 2. Identifying like terms is crucial for combining them during polynomial addition or subtraction.

Combining Polynomials

Combining polynomials involves adding or subtracting their like terms to simplify the expression. This process requires careful attention to the coefficients of like terms, ensuring that they are summed correctly. The result is a new polynomial that retains the same variable structure but has simplified coefficients.