The Product of 3a 2 4a2 2a 9
What is the Product of 3a 2 4a2 2a 9?
The product of 3a 2 4a2 2a 9 is a mathematical expression that involves the multiplication of several terms. To find the product, we need to follow the order of operations (PEMDAS) and multiply each term separately.
Step 1: Multiply the Coefficients
The coefficients are the numbers in front of the variables. In this case, the coefficients are 3, 2, 4, and 9. We multiply these coefficients together to get the product of the coefficients.
- 3 × 2 = 6
- 6 × 4 = 24
- 24 × 2 = 48
- 48 × 9 = 432
Step 2: Multiply the Variables
The variables are the terms inside the parentheses. In this case, the variables are a, 2, a, and 9. We multiply each variable together to get the product of the variables.
- a × 2 = 2a
- 2a × a = 2a2
- 2a2 × 9 = 18a2
- 18a2 × a = 18a3
Step 3: Combine the Products
Now that we have the products of the coefficients and variables, we can combine them to get the final product.
- 3a 2 4a2 2a 9 = 432 × 2a2 × 18a3
The Final Answer
The product of 3a 2 4a2 2a 9 is 432 × 2a2 × 18a3.
Important Points to Remember
- When multiplying coefficients, we multiply the numbers in front of the variables.
- When multiplying variables, we multiply the variables together.
- When combining products, we multiply the coefficients and add the exponents of the variables.
Example Walkthrough
Let’s take an example to illustrate the process.
Suppose we want to find the product of 2a 3a 4a 5.
- Multiply the coefficients: 2 × 3 = 6
- Multiply the variables: a × a = a2
- Combine the products: 6a2 × 4a 5 = 24a3 × 5 = 120a3
Table: Multiplication of Coefficients
| Coefficient | Product |
|---|---|
| 3 | 3 |
| 2 | 2 |
| 4 | 4 |
| 9 | 9 |
Table: Multiplication of Variables
| Variable | Product |
|---|---|
| a | a |
| 2a | 2a |
| a2 | a2 |
| 9a | 9a |
Conclusion
The product of 3a 2 4a2 2a 9 is a mathematical expression that involves the multiplication of several terms. By following the order of operations and multiplying each term separately, we can find the final product. The product is 432 × 2a2 × 18a3.