Verified Answer :

  • Calculate the sum of the original expression: \(26 + 18 = 44\).
  • Expand each provided option using the distributive property: \(2(12 + 8) = 40\), \(2(12 + 9) = 42\), \(2(14 + 9) = 46\), and \(2(14 + 8) = 44\).
  • Identify that the only expression resulting in 44 is \(2(14 + 8)\).
  • Conclude that the factored expression is \(\boxed{2(14 + 8)}\).

Explanation

  1. Analyze the Problem and Evaluate the Sum

The expression to consider is \(26 + 18\). First, we calculate the sum: \(26 + 18 = 44\). Our goal is to identify which of the given expressions, when factored by \(2\), results in this sum. The provided options are \(2(12 + 8)\), \(2(12 + 9)\), \(2(14 + 9)\), and \(2(14 + 8)\).

  1. Evaluate the Options

We expand each of the given expressions using the distributive property, which states that \(a(b + c) = ab + ac\), to see which one evaluates to \(44\):

  • For \(2(12 + 8)\): \(2 \times 12 + 2 \times 8 = 24 + 16 = 40\).
  • For \(2(12 + 9)\): \(2 \times 12 + 2 \times 9 = 24 + 18 = 42\).
  • For \(2(14 + 9)\): \(2 \times 14 + 2 \times 9 = 28 + 18 = 46\).
  • For \(2(14 + 8)\): \(2 \times 14 + 2 \times 8 = 28 + 16 = 44\).

We can see that the expression \(2(14 + 8)\) is equivalent to the sum \(26 + 18\).

  1. Conclusion

Comparing the original sum \(44\) with the values calculated from the expressions, only \(2(14 + 8)\) yields \(44\). Thus, this expression shows a valid way to factor the sum \(26 + 18\). The final answer is \(\boxed{2(14 + 8)}\).

Examples

Factoring is a fundamental skill in algebra that simplifies complex expressions. For example, if you are organizing a total of 44 items into two equal boxes, you can represent this as dividing the total sum into smaller parts to manage them more easily. If you have 28 items in one category and 16 items in another, you can represent the total as \(28 + 16 = 2(14 + 8)\), showing that you have 2 groups, each containing 14 items of the first type and 8 items of the second. This helps in visualising how to split resources effectively.