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Polynomials are algebraic expressions consisting of variables, constants, and exponents. They include operations such as addition, subtraction, multiplication, and non-negative integer exponents. For example, in the polynomial expression \(9m^{3} - 5m^{2} + 4m - 8\), each part separated by a plus or minus sign is called a term.
Polynomials are categorized based on their degree, which is the highest power of the variable in the expression. For instance, in the polynomial \(9m^{3}\text{,}\) the highest power of \(m\) is 3, so it is called a cubic polynomial.
Understanding polynomials is crucial for solving algebraic problems because they form the foundation for more complex operations, such as polynomial addition.

An algebraic expression is a combination of numbers, variables, and at least one arithmetic operation (such as addition or subtraction). Unlike an equation, it does not have an equals sign.
For example, consider \(9m^{3} - 5m^{2} + 4m - 8\). This is an algebraic expression because it has variables \(m\), numbers (coefficients), and operations (addition and subtraction).
It is crucial to learn how to manipulate algebraic expressions, as they help in solving various mathematical problems. Simplifying and performing operations on algebraic expressions pave the way for understanding more intricate algebraic concepts.

Combining like terms is a fundamental step in simplifying algebraic expressions. Terms are 'like' if they have the same variables raised to the same powers. For example, the terms \(9m^{3}\) and \(-3m^{3}\) are like terms because they both involve \(m^{3}\).
To combine like terms, you add or subtract their coefficients while keeping the variable part the same. This process simplifies the expression and makes it easier to solve or manipulate.
In our given problem, we combined like terms as follows:

• \(9m^{3} + (-3m^{3}) = 6m^{3}\)
• \(-5m^{2} + 6m^{2} = m^{2}\)
• \(4m + 0m = 4m\)
• \(-8 + (-6) = -14\)

By mastering the skill of combining like terms, you can handle more complex polynomial expressions with ease.