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Combining like terms is a fundamental concept in algebra. When we talk about 'like terms', we mean terms that have the same variable raised to the same power. In our exercise, we have two sets of like terms: - Terms involving \(p^2\), which are \(2p^2\) and \(3p^2\). - Terms involving \(p^3\), which are \(-8p^3\) and \(-6p^3\). To combine like terms, add or subtract their coefficients. For \(p^2\), add 2 and 3, resulting in 5. For \(p^3\), add -8 and -6, resulting in -14. Thus, the simplified form of \(2p^2 + 3p^2 - 8p^3 - 6p^3\) is \(5p^2 - 14p^3\). When combining like terms, double-check your coefficients to ensure accuracy.

A polynomial is an algebraic expression that consists of variables, coefficients, and exponents. Each term in a polynomial is a product of a coefficient and a variable raised to an exponent. For instance, in our exercise, \(2p^2\) is a term with a coefficient of 2 and an exponent of 2 applied to the variable \(p\). Polynomials can have multiple terms. They are usually written in standard form, which means ordering the terms from the highest exponent to the lowest. In our simplified expression \(5p^2 - 14p^3\), it would be more appropriately written as \(-14p^3 + 5p^2\). Polynomials are foundational in algebra and are used in a variety of mathematical contexts, from solving equations to modeling real-world scenarios.

Exponents denote the number of times a number (the base) is multiplied by itself. In our context, consider \(p^2\) and \(p^3\). Here, \(p^2\) represents \(p\) multiplied by itself once, and \(p^3\) represents \(p\) multiplied by itself twice. When adding or subtracting terms with exponents, the exponents must remain the same; only the coefficients are combined. This is crucial for correctly simplifying expressions. In our exercise, since \(2p^2\) and \(3p^2\) have the same exponent (2), we combine them directly. Similarly, we combine \(-8p^3\) and \(-6p^3\) because they share the same exponent (3). Remember, you cannot combine terms with different exponents. Thus, \(p^2\) and \(p^3\) will always remain separate terms in a polynomial.