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When adding polynomials, the key is to focus on grouping and combining like terms. But what exactly are "like terms"? Essentially, they are terms in a polynomial that have the same variables raised to the same power. Consider a term like - \(3a^2\)In this term, "\(a\)" is raised to the power of 2.Because of this, it can only be combined with other terms that have "\(a^2\)".This is crucial when adding polynomials - You must only combine terms that are alike.For example, in the exercise, you needed to add \(3a^2\) with \(2a^2\) because they both have the variable "a" raised to the same power, which is 2.Employing this tactic ensures that you do not mix terms incorrectly, like adding terms with different powers or entirely different variables. By identifying and focusing on like terms, - Simplifying polynomial expressions becomes much more manageable.

A coefficient is the numerical part of a term. When combining like terms, this is the part that you add or subtract. In our polynomial exercise, terms like \(3a^2\) have a coefficient of 3. You can think of coefficients as weights that tell you how much of each "bit" you have.To properly combine terms, you - need to add or subtract the coefficients of terms that are alike. For instance, for terms including \(a\), the coefficients are -4 and -5. By adding them, you get -9 for the combined term.So, knowing how to handle coefficients is crucial:- They tell you how many times each term is counted in your expression.Without understanding coefficients, it would be challenging to properly combine terms or simplify polynomials.

A polynomial expression is simply a mathematical phrase made up of terms. These terms can include numbers, variables, and powers. In the realm of our exercise, we were given two distinct polynomials:- \((3a^2 - 4a + 2)\)- \((2a^2 - 5a + 6)\)Each consists of terms with coefficients and variables, and these terms can get complex.To simplify or add polynomial expressions, - Start by identifying the like terms.Then, use the coefficients to combine these terms, yielding a simplified polynomial expression.The end result in our exercise was: - \(5a^2 - 9a + 8\)This outcome is much simpler and concise. Working with polynomial expressions requires practice, but once you grasp the fundamentals, it becomes a lot easier!