Explain why the expression 6 + 2(x - 4) is not in simplest form.

Explain why the expression 6 + 2(x - 4) is not in simplest form.

• A. The 2 has not been distributed to the terms in the parentheses.
• B. The expression contains too many parentheses.
• C. The expression is already simplified.
• D. The coefficients are not integers.

Answer: (B)

Distributing the outside factor is the step that often makes expressions simpler. Here, 2 is multiplying the whole inside, so apply the distributive property: 2(x - 4) becomes 2x - 8. Then you have 6 + 2x - 8, which combines to 2x - 2. So the original expression isn’t in simplest form because the distribution hasn’t been done yet. It’s not about the number of parentheses—removing them is done by distributing. It’s not already simplified, since 6 and -8 can be combined to -2, and the result 2x - 2 is the concise form. The issue isn’t the coefficients being integers; the key is that distributing the 2 across the parentheses is needed.

Distributing the outside factor is the step that often makes expressions simpler. Here, 2 is multiplying the whole inside, so apply the distributive property: 2(x - 4) becomes 2x - 8. Then you have 6 + 2x - 8, which combines to 2x - 2. So the original expression isn’t in simplest form because the distribution hasn’t been done yet.

It’s not about the number of parentheses—removing them is done by distributing. It’s not already simplified, since 6 and -8 can be combined to -2, and the result 2x - 2 is the concise form. The issue isn’t the coefficients being integers; the key is that distributing the 2 across the parentheses is needed.