Calculate 2a² + 3c For A = 3, B = -2, C = -1 Step By Step Solution

Hey guys! Today, we're diving into a fun little math problem. We need to calculate the value of the expression 2a² + 3c given that a = 3, b = -2, and c = -1. Don't worry, it's simpler than it looks! We'll break it down step by step, so you can easily follow along and understand how we arrive at the final answer.

Understanding the Expression

Before we start plugging in the numbers, let's take a closer look at the expression 2a² + 3c. This expression consists of two terms: 2a² and 3c. Each term involves variables (a and c) and constants (2 and 3). The variable a is squared, meaning it's multiplied by itself. Understanding these components is crucial for correctly solving the problem.

The first term, 2a², means we need to square the value of a (multiply it by itself) and then multiply the result by 2. The second term, 3c, simply means we need to multiply the value of c by 3. Once we calculate each term separately, we'll add them together to get the final result. Remember, the order of operations (PEMDAS/BODMAS) is important here: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). In this case, we'll deal with the exponent first, then the multiplications, and finally the addition.

It's also important to pay attention to the signs of the numbers. Negative numbers can sometimes trip us up, so we need to be careful when multiplying and adding them. In this problem, we have a negative value for c, which means we'll be dealing with a negative term when we calculate 3c. Keeping track of these details will help us avoid making mistakes and ensure we get the correct answer. So, let's get started with the calculations!

Step-by-Step Calculation

Okay, let's get our hands dirty and plug in the values! We have a = 3 and c = -1, so we'll substitute these into the expression 2a² + 3c. This gives us 2(3)² + 3(-1). Remember, the first step is to deal with the exponent. So, what is 3 squared? It's 3 multiplied by itself, which is 3 * 3 = 9. Now our expression looks like this: 2(9) + 3(-1).

Next up, we need to perform the multiplications. We have 2 * 9 and 3 * -1. Let's start with 2 * 9. That's simply 18. Now, let's tackle 3 * -1. Remember that multiplying a positive number by a negative number results in a negative number. So, 3 * -1 = -3. Our expression now looks like this: 18 + (-3).

Finally, we have an addition to perform. We're adding a negative number, which is the same as subtracting. So, 18 + (-3) is the same as 18 - 3. And what's 18 minus 3? It's 15! So, after all the calculations, we've found that the value of the expression 2a² + 3c when a = 3 and c = -1 is 15. But wait! We don't see 15 as one of the answer choices. Let's double-check our work to make sure we didn't make any silly mistakes. It's always a good idea to review your steps, especially in math problems.

Let's go through the calculation again, making sure we haven't missed anything. 2a² + 3c with a = 3 and c = -1 becomes 2(3)² + 3(-1). 3 squared is indeed 9, so we have 2(9) + 3(-1). 2 times 9 is 18, and 3 times -1 is -3. So, we have 18 + (-3), which is 18 - 3. And that equals 15. Hmm, we still get 15. It seems there might be a mistake in the answer choices provided. Our calculation is correct, so the answer should be 15.

Identifying the Correct Answer

Alright, so we've diligently calculated the expression 2a² + 3c for the given values of a and c, and we've arrived at the answer 15. However, when we look at the answer choices, we notice something's amiss. The options provided are:

• A) 12
• B) 6
• C) 0
• D) -6

None of these match our calculated result of 15. This situation can be a bit perplexing, but it's crucial to remain calm and methodical. Let's analyze what could be happening here. There are a few possibilities to consider.

Firstly, it's possible that there's a mistake in the answer choices themselves. This isn't uncommon, especially in multiple-choice questions. Sometimes, errors can creep in during the creation or transcription of the options. Secondly, there's a slight chance we might have made a mistake in our calculations, even though we've double-checked them. It's always wise to be thorough and review our steps again, just to be absolutely sure. However, having gone through the process multiple times, we're quite confident in our result.

Given these possibilities, the most logical course of action is to trust our calculations. We've followed the correct order of operations, substituted the values accurately, and arrived at a consistent answer of 15. Therefore, the most likely explanation is that there's an error in the provided answer choices. In a real-world scenario, such as a test or exam, it would be advisable to bring this discrepancy to the attention of the instructor or invigilator. It's essential to ensure that the correct answer is acknowledged, even if it's not explicitly listed among the options. So, based on our calculations, the correct answer is 15, which is not among the options provided.

Conclusion

So, guys, we tackled a math problem today and learned how to calculate the value of an expression by substituting given values for variables. We carefully followed the order of operations and arrived at our answer. Remember, it's always a good idea to double-check your work to avoid making mistakes. And sometimes, even when you've done everything right, there might be a mistake in the answer choices themselves. In such cases, it's important to trust your calculations and, if possible, bring the issue to the attention of the relevant authority.

In this case, we found that the value of the expression 2a² + 3c for a = 3 and c = -1 is 15. However, 15 wasn't among the answer choices. This highlights the importance of critical thinking and not blindly choosing an option just because it's there. Always be sure to understand the problem, perform the calculations accurately, and analyze the results logically. Keep practicing, and you'll become a math whiz in no time!

Therefore, the correct answer is 15, which is not listed in the options.

Repair Input Keyword: Calculate the value of the expression 2a² + 3c when a = 3, b = -2, and c = -1. What is the final result?

Keywords: Calculate expression, 2a² + 3c, math problem, step-by-step calculation, correct answer, order of operations, substitute values, variables, constants, negative numbers, multiplication, addition, exponents, answer choices, critical thinking, mathematical expression.