Question
Which of the following is the correct simplification of the expression below? \( 20-18+2 \times 3+(6-7)^{2} \)
Ask by Mejia Bob. in the United States
Dec 30,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified result of the expression \( 20 - 18 + 2 \times 3 + (6 - 7)^{2} \) is \( 9 \).
Solution
To simplify the expression \( 20 - 18 + 2 \times 3 + (6 - 7)^{2} \), we'll follow the order of operations, often remembered by the acronym PEMDAS:
1. **P**arentheses
2. **E**xponents
3. **M**ultiplication and **D**ivision (from left to right)
4. **A**ddition and **S**ubtraction (from left to right)
Let's break it down step-by-step:
1. **Parentheses**:
\[
(6 - 7) = -1
\]
So, the expression becomes:
\[
20 - 18 + 2 \times 3 + (-1)^{2}
\]
2. **Exponents**:
\[
(-1)^{2} = 1
\]
Now, the expression is:
\[
20 - 18 + 2 \times 3 + 1
\]
3. **Multiplication**:
\[
2 \times 3 = 6
\]
Updating the expression:
\[
20 - 18 + 6 + 1
\]
4. **Addition and Subtraction** (from left to right):
- First, subtract:
\[
20 - 18 = 2
\]
- Then, add:
\[
2 + 6 = 8
\]
- Finally, add:
\[
8 + 1 = 9
\]
**Final Simplified Result:** \( 9 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
Let's break this down step by step! First, we follow the order of operations (PEMDAS/BODMAS). Start with the parentheses: \( (6-7)^{2} = (-1)^{2} = 1 \). Next, handle the multiplication: \( 2 \times 3 = 6 \). Now substitute these values back into the expression: \( 20 - 18 + 6 + 1 \). Now, proceed with addition and subtraction from left to right: 1. \( 20 - 18 = 2 \) 2. \( 2 + 6 = 8 \) 3. \( 8 + 1 = 9 \) So, the correct simplification of the expression \( 20 - 18 + 2 \times 3 + (6 - 7)^{2} \) is \( 9 \).
