Evaluating 1.2x³ - 2.7y² For X=3 And Y=2 - A Step-by-Step Guide
Hey guys! Today, we're going to dive into a fun algebra problem. We've got this expression: 1.2x³ - 2.7y², and we need to figure out what it equals when x is 3 and y is 2. Don't worry, it's not as scary as it looks! We'll break it down step-by-step so it's super easy to follow. Algebra can seem tricky at first, but with a little practice, you'll be solving these problems like a pro in no time. The key is to understand the order of operations and how to substitute values into the expression correctly. So, let's get started and unlock the mystery of this algebraic expression together!
Understanding the Expression
Before we jump into plugging in the numbers, let's take a closer look at the expression 1.2x³ - 2.7y². What does it actually mean? Well, in algebra, we often use letters like x and y to represent numbers. These are called variables because their values can vary. In this case, we're told that x is 3 and y is 2. The expression also includes exponents, which are those little numbers written up high. The exponent tells us how many times to multiply the base number by itself. For example, x³ means x multiplied by itself three times (x * x* * x*). Similarly, y² means y multiplied by itself two times (y * y*). We also have coefficients, which are the numbers in front of the variables (1.2 and 2.7 in this case). These coefficients are multiplied by the variable terms. Understanding these components is crucial for correctly evaluating the expression. We need to follow the order of operations (PEMDAS/BODMAS) to ensure we get the right answer. This means we handle parentheses (or brackets), exponents, multiplication and division (from left to right), and addition and subtraction (from left to right) in that specific order. So, with a clear understanding of the expression's parts, we're well-prepared to move on to the next step, which involves substituting the given values of x and y into the expression. Let's keep going and see how it all comes together!
Step 1: Substituting the Values
Okay, the first thing we need to do is replace the variables x and y with their given values. Remember, we're told that x = 3 and y = 2. So, wherever we see an x in the expression, we'll put a 3, and wherever we see a y, we'll put a 2. This is called substitution, and it's a fundamental step in solving algebraic expressions. After substituting the values, our expression 1.2x³ - 2.7y² will look like this: 1.2(3)³ - 2.7(2)². Notice how we've replaced the x with a 3 and the y with a 2. The parentheses are important here because they indicate that we need to multiply the coefficient by the value of the variable raised to the power. Now that we've substituted the values, we're ready to move on to the next step, which involves dealing with the exponents. We need to calculate the values of 3³ and 2² before we can perform any other operations. So, let's keep going and see how to handle those exponents!
Step 2: Evaluating the Exponents
Alright, now it's time to tackle those exponents! Remember, an exponent tells us how many times to multiply a number by itself. So, 3³ means 3 * 3 * 3, and 2² means 2 * 2. Let's calculate these values. 3 * 3 * 3 is 27. So, 3³ = 27. And 2 * 2 is 4. So, 2² = 4. Now we can replace 3³ with 27 and 2² with 4 in our expression. Our expression 1.2(3)³ - 2.7(2)² now becomes 1.2(27) - 2.7(4). We've successfully evaluated the exponents, and our expression is looking simpler already! We're one step closer to finding the final answer. The next step involves performing the multiplication operations. We need to multiply 1.2 by 27 and 2.7 by 4 before we can do the subtraction. So, let's move on to the next step and get those multiplications done!
Step 3: Performing the Multiplication
Okay, let's get multiplying! We have two multiplication operations to perform: 1.2 multiplied by 27 and 2.7 multiplied by 4. Let's start with 1.2 * 27. If you do the math, you'll find that 1.2 * 27 = 32.4. Now, let's move on to the second multiplication: 2.7 * 4. When you multiply 2.7 by 4, you get 10.8. So, 2.7 * 4 = 10.8. Now we can replace 1.2(27) with 32.4 and 2.7(4) with 10.8 in our expression. Our expression 1.2(27) - 2.7(4) now becomes 32.4 - 10.8. We've successfully performed the multiplication operations, and we're down to just one operation left: subtraction. We're almost there! The final step is to subtract 10.8 from 32.4 to get our final answer. So, let's move on to the last step and wrap this up!
Step 4: Subtraction to Get the Final Answer
We've reached the final step, guys! We need to subtract 10.8 from 32.4. This is a straightforward subtraction problem. If you subtract 10.8 from 32.4, you get 21.6. So, 32.4 - 10.8 = 21.6. That's it! We've successfully evaluated the expression 1.2x³ - 2.7y² when x = 3 and y = 2. The final answer is 21.6. We did it! We took a seemingly complex algebraic expression and broke it down into manageable steps. We substituted the values, evaluated the exponents, performed the multiplication, and finally, did the subtraction. Each step was crucial in getting us to the correct answer. Remember, the key to solving these kinds of problems is to take it one step at a time and follow the order of operations. Now that we've solved this problem together, you'll be much more confident in tackling similar algebraic challenges in the future. Great job, everyone! You're becoming algebra whizzes!
Final Result
So, after all our hard work, we've arrived at the final answer. When we substitute x = 3 and y = 2 into the expression 1.2x³ - 2.7y², we get 21.6. This means that the value of the expression is 21.6 when x and y have those specific values. We've successfully navigated through the steps of substitution, exponent evaluation, multiplication, and subtraction to reach this result. It's a great feeling to solve a problem like this, and it shows that you're developing a strong understanding of algebraic concepts. Remember, algebra is all about working with symbols and numbers to solve problems, and you've just demonstrated your ability to do that. Keep practicing, and you'll continue to improve your skills and confidence in algebra. You've got this! Congratulations on solving this problem and reaching the final result of 21.6!
