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The question asks to represent \(50 + 30\) as a product of two factors. Let's break down the sum:

\[
50 + 30 = 80
\]

To factor this sum, we need to find an expression where two numbers multiply to form 80.

We can observe that:
\[
50 = 5 \times 10 \quad \text{and} \quad 30 = 5 \times 6
\]

So, the common factor between \(50\) and \(30\) is \(5\), which leads us to the expression:
\[
50 + 30 = 5(10 + 6)
\]

Looking at the options provided:
1. \(5(10 + 3)\) → Incorrect, as \(10 + 3 = 13\), not \(80\).
2. \(10(5 + 2)\) → Incorrect, as \(5 + 2 = 7\), and \(10 \times 7 = 70\), not \(80\).
3. \(10(5 + 3)\) → **Correct**, because \(5 + 3 = 8\), and \(10 \times 8 = 80\).
4. \(5(10 + 7)\) → Incorrect, as \(10 + 7 = 17\), not \(80\).

Thus, the correct expression is **\(10(5 + 3)\)**.

Would you like further details on how this factorization works? Here are some related questions to expand on this:

1. How do you find the greatest common factor of two numbers?
2. What other ways can you factor a sum like \(50 + 30\)?
3. Can you explain the distributive property in more detail?
4. How can factoring help in solving algebraic equations?
5. What is the difference between factoring a sum and factoring a product?

**Tip:** Always check if both numbers in a sum share a common factor before factoring!

Which expression shows 50 + 30 written as a product of two factors?

Learn how to factor the sum 50 + 30 into a product of two factors using the distributive property. This problem is suitable for students in grades 6-8 and covers fundamental algebraic concepts like factoring and the distributive property.

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