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When dealing with polynomial addition, one of the first concepts you'll encounter is "like terms." Like terms are components within algebraic expressions that have the same variable raised to the same power. Why is this important? Because you can only combine terms with matching components. For instance, in the exercise, the terms \(2d^5\) and \(10d^5\) are considered like terms because they both have the variable \(d\) raised to the fifth power.
Another example from the problem includes \(\frac{1}{3}d^4\) and \(-2d^4\). Even though their coefficients differ, they both involve \(d^4\). Recognizing like terms is the first step in effectively combining terms in any algebraic expression.

The term "coefficients" refers to the numerical factor present in terms of an algebraic expression. In our exercise, each polynomial term like \(2d^5\), \(\frac{1}{3}d^4\), and \(9d^2\) features a coefficient. This coefficient is multiplied by the variable component.
For example, in \(2d^5\), the coefficient is \(2\), and in \(-2d^4\), it is \(-2\). Coefficients provide the weight or amount of a term within an expression. They are crucial in operations such as adding or subtracting like terms, as these operations solely involve manipulating the coefficients.

Combining terms, especially like terms, is all about simplifying polynomial expressions. After identifying the like terms, the next step is adding or subtracting their coefficients. For example, \(2d^5\) and \(10d^5\) are combined by adding their coefficients to get \(12d^5\).
In our exercise, \(\frac{1}{3}d^4 - 2d^4\) becomes \(-\frac{5}{3}d^4\) upon calculating their coefficient difference. Furthermore, constants such as \(-11\) and \(4\) combine to yield \(-7\). Always remember, terms that are not like cannot be combined; they remain unchanged unless paired with similar terms from other expressions.

Expressions in algebra can be seen as a set of terms which include variables, constants, and coefficients combined by operations such as addition or subtraction. The given exercise involves adding two polynomial expressions: \(2d^{5}+\frac{1}{3}d^{4}-11\) and \(10d^{5}-2d^{4}+9d^{2}+4\).
Each term within expressions serves a role, and the challenge is to simplify them by using operations to make them more manageable. When you explore an expression, look for opportunities to condense it by locating and operating on like terms and considering the role of each term based on its coefficient and variable power. This understanding makes handling larger, more complex expressions much simpler.