Verified Answer :

  • Calculate the sum of the original expression: \(120 + 20 = 140\).
  • Evaluate each option to compare:
  • \(20(5 + 24) = 580\)
  • \(10(10 + 2) = 120\)
  • \(6(114 + 14) = 768\)
  • \(5(24 + 4) = 140\)
  • Identify the equivalent expression as \(\boxed{5(24 + 4)}\).

Explanation

  1. Evaluating the Expression and Options

The objective is to rewrite the expression \(120 + 20\) using factoring to identify which of the provided options is equivalent to it. First, we calculate the total sum of the original expression:
\[120 + 20 = 140.\]
Next, we evaluate each of the given options to determine which one results in the same value:

  1. \(20(5 + 24) = 20 \times 29 = 580\)
  2. \(10(10 + 2) = 10 \times 12 = 120\)
  3. \(6(114 + 14) = 6 \times 128 = 768\)
  4. \(5(24 + 4) = 5 \times 28 = 140\)

By comparing the results, we find that the fourth option, \(5(24 + 4)\), is equal to 140, matching the original expression.

  1. Final Conclusion

After evaluating the original expression \(120 + 20 = 140\) and checking each option, we determined that \(5(24 + 4) = 5 \times 28 = 140\). Therefore, the factored form of the expression is \(5(24 + 4)\). The final answer is \(\boxed{5(24 + 4)}\).

Examples

Factoring is a powerful tool used to simplify expressions or make calculations easier. For example, if you are buying 5 packs of items where each pack contains 24 of one type and 4 of another type, the total cost or count can be represented as \(5(24 + 4)\). This is much easier to manage than calculating each component individually. Understanding how to distribute and factor numbers helps in mental math, inventory management, and simplifying complex algebraic problems.

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