Simplify each expression. Justify each step.

1. (12 + 8x) + 13
2. (7-7) +12
3. (5 * m) * 7

1 answer

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. \( (5 * m) * 7 = 35m \)