Question

Simplify each expression. Justify each step.
1. (12 + 8x) + 13
2. (7-7) +12
3. (5 * m) * 7

Answer 1

Let's simplify each expression step by step:

### 1. Simplifying \( (12 + 8x) + 13 \)

**Step 1:** Identify like terms.
The expression contains constants and a variable term.

**Step 2:** Combine the constant terms, \( 12 \) and \( 13 \).
So, we have:
\[ 12 + 13 = 25 \]

**Step 3:** Rewrite the expression:
\[ (12 + 8x) + 13 = 25 + 8x \]

**Final Result:**
\[ (12 + 8x) + 13 = 25 + 8x \]

### 2. Simplifying \( (7 - 7) + 12 \)

**Step 1:** Simplify \( 7 - 7 \) first.
Since \( 7 - 7 = 0 \):

**Step 2:** Rewrite the expression:
\[ (7 - 7) + 12 = 0 + 12 \]

**Step 3:** Combine the result with the constant:
\[ 0 + 12 = 12 \]

**Final Result:**
\[ (7 - 7) + 12 = 12 \]

### 3. Simplifying \( (5 * m) * 7 \)

**Step 1:** Use the associative property of multiplication, which says that changing the grouping of factors does not change the product.
So, we can regroup as follows:
\[ (5 * m) * 7 = 5 * (m * 7) \]

**Step 2:** Rewrite the expression.
Thus, we have:
\[ 5m * 7 \]

**Step 3:** Multiply these terms using properties of multiplication:
\[ 5 * 7 = 35 \], so we can combine:
\[ 5m * 7 = 35m \]

**Final Result:**
\[ (5 * m) * 7 = 35m \]

In summary:
1. \( (12 + 8x) + 13 = 25 + 8x \)
2. \( (7 - 7) + 12 = 12 \)
3. \( (5 * m) * 7 = 35m \)