Solving Math: $\left((-4)^2-2\right) \times(-3)$

Nov 5, 2025 by Admin 49 views

$Solving $\left((-4)^2-2\right) \times(-3)$: A Step-by-Step Guide$

Hey math enthusiasts! Let's dive into solving the mathematical expression $\left((-4)^2-2\right) \times(-3)$ . This problem is a great way to brush up on our order of operations, dealing with negative numbers, and mastering numerical expressions. Don't worry, it's not as scary as it looks. We'll break it down step by step to make it super clear and easy to understand. So, grab your calculators (or not, if you're feeling brave!), and let's get started. Remember, the key to solving these types of problems is to be patient and methodical. Take your time, and make sure you understand each step before moving on to the next. That way, you'll not only solve this particular problem but also build a solid foundation for tackling more complex math problems in the future. We'll be using the PEMDAS/BODMAS rule – Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right) – to guide us. Let's start with the first step which is simplifying the term in the parenthesis.

Step 1: Parentheses and Exponents

Alright guys, the first thing we need to do is focus on what's inside the parentheses: $\left((-4)^2-2\right)$ . According to PEMDAS/BODMAS, we first need to handle the exponents. So, let's look at $(-4)^2$ . Remember, when you square a negative number, the result is positive. This is because a negative number multiplied by another negative number results in a positive number. In this case, $(-4)^2$ means $(-4) \times (-4)$ , which equals 16. So, we simplify the expression inside the parentheses to $(16 - 2)$ . Great job, everyone! We've successfully handled the exponent. Now our expression looks like this: $(16-2) \times (-3)$ . Always remember, the order of operations is crucial. Doing the exponent before anything else is what makes the problem flow correctly. This ensures we get the right answer and don't end up with a mathematical mess. Another important thing to keep in mind is the sign of the numbers. Pay close attention to whether a number is positive or negative, because this will significantly affect your calculations.

Now, let's keep going. We've dealt with the exponent, so we move on to the next operation within the parentheses, which is subtraction. Let's proceed to the next step which is simplification.

Simplifying the Parentheses

Now, let's simplify the expression within the parentheses, we have $(16 - 2)$ . This is a simple subtraction problem. 16 minus 2 is equal to 14. So, we now have 14 inside the parentheses. Our expression has now simplified to $14 \times (-3)$ . See? We're making great progress! We started with a slightly complex expression, and now we're down to a straightforward multiplication problem. Always remember to check your work at each step. This can prevent small errors from snowballing into a larger problem later on. And don't be afraid to ask for help if you're stuck! Math can be challenging, but with persistence and the right approach, anyone can master it. Keep in mind that we're following the order of operations, step by step. That is why it is so important that we handle the parenthesis first before we do any multiplication. Also, note that we have completed all the operation that we needed to do inside the parenthesis.

Now, we move on to the next step, which involves the multiplication.

Step 2: Multiplication

We're now at the final step, guys! We've simplified the expression inside the parentheses, and now we just have a simple multiplication to do. We need to multiply $14 \times (-3)$ . Remember that when you multiply a positive number by a negative number, the result is negative. So, $14 \times (-3)$ will give us a negative answer. Now, let's do the multiplication: $14 \times 3 = 42$ . Since one of the numbers is negative, our final answer is -42. And there you have it! We've successfully solved the expression $\left((-4)^2-2\right) \times(-3)$ , and the answer is -42. Amazing work, everyone! You've successfully navigated through the order of operations, exponents, and negative numbers. Give yourselves a pat on the back. Remember that practice makes perfect, and the more you work through these types of problems, the easier they will become. You can try solving similar problems, changing the numbers, or adding more steps to test your understanding. The goal is to build your confidence and become more comfortable with mathematical expressions.

Final Answer

So, the solution to $\left((-4)^2-2\right) \times(-3)$ is -42. We arrived at this answer by:

Simplifying the Exponent: $(-4)^2 = 16$
Simplifying inside the Parentheses: $16 - 2 = 14$
Multiplying: $14 \times (-3) = -42$

That's it! You've now conquered this math problem. Keep up the great work, and don't hesitate to practice more problems to sharpen your skills. And remember, the journey of learning math is a rewarding one. Keep going!

Important Tips and Tricks

Let's get some extra important tips and tricks to help you with these kinds of problems, shall we?

Memorize PEMDAS/BODMAS: This is your guiding principle. Always remember the order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Practice, Practice, Practice: The more you solve these problems, the more comfortable you'll become. Work through different examples to get a better understanding. Try different types of problems and always check your answers.
Pay Attention to Signs: Be very careful with positive and negative numbers. Remember the rules: negative times negative equals positive, negative times positive equals negative, and positive times positive equals positive.
Break Down the Problem: If the expression looks complex, break it down into smaller, more manageable steps. This will make it less intimidating and easier to solve.
Use a Calculator (Initially): Don't be afraid to use a calculator. It can help you check your work and ensure you're on the right track. As you get more comfortable, try to do more calculations in your head.
Double-Check Your Work: Always review your steps to avoid careless mistakes. It's easy to make a small error, and double-checking can save you time and frustration.
Seek Help: If you get stuck, don't hesitate to ask a teacher, friend, or family member for help. Sometimes, a fresh perspective can make all the difference.
Understand the Concepts: Don't just memorize the steps. Make sure you understand why you're performing each operation. This deeper understanding will help you in the long run.

By following these tips and practicing regularly, you'll become a math whiz in no time. Keep up the great work and enjoy the journey!

Conclusion

In conclusion, solving the expression $\left((-4)^2-2\right) \times(-3)$ is a straightforward process when you break it down into manageable steps. We've seen how important it is to follow the order of operations and to be mindful of negative numbers. By carefully handling the exponent, simplifying the expression within the parentheses, and then performing the multiplication, we arrived at the correct answer of -42. Remember, guys, math isn't just about getting the right answer; it's about the journey of problem-solving. It's about developing critical thinking skills and building a strong foundation for future mathematical endeavors. So, keep practicing, keep learning, and keep challenging yourselves. The world of mathematics is vast and fascinating, and there's always something new to discover. Keep this in mind when you're working through math problems. Take it step by step, and don't get discouraged if it seems tough at first. Remember that every problem you solve is a victory, and each step forward brings you closer to mastering the subject. The more you immerse yourself in the world of math, the more enjoyable and rewarding it will become. Embrace the challenges, learn from your mistakes, and celebrate your successes. You've got this!