- Identify the coefficients of the given expression: 6 and 2.
- Recognize that \(x^3\) and \(x^3\) are like terms, so their exponents remain the same.
- Sum the coefficients: \(6 + 2 = 8\).
- Combine the results to get the simplified expression: \(\boxed{8}x^{\boxed{3}}\).
Explanation
- Simplifying the Expression
The goal is to simplify the expression \(6x^3 + 2x^3\) into the form \(Ax^n\). Both terms contain the same variable part, \(x^3\), which means they are "like terms." To add like terms, we simply add their coefficients while keeping the variable and exponent unchanged. The coefficient of the first term is 6, and the coefficient of the second term is 2. Therefore, the sum of the coefficients is \(6 + 2 = 8\). The variable part \(x^3\) remains the same. Thus, the simplified expression is \(8x^3\). Comparing this to the form \(Ax^n\), we find \(A = 8\) and \(n = 3\).
Examples
Imagine you are stocking shelves with toy sets. If you have 6 boxes of a particular set (where each box contains \(x^3\) items) and you receive 2 more boxes of the same set, the total number of boxes is \(6 + 2 = 8\). Since each box still contains \(x^3\) items, the total number of items is \(8x^3\). This illustrates how we combine like terms in algebra to simplify calculations in real-world inventory or resource management.