The Product of 3a+5 and 2a2+4a-2
What is the Product of 3a+5 and 2a2+4a-2?
When we multiply two polynomials, we need to follow a specific set of rules to find the product. In this article, we will explore the product of 3a+5 and 2a2+4a-2.
Step 1: Multiply Each Term
To find the product, we need to multiply each term in the first polynomial by each term in the second polynomial.
3a × 2a2 = 6a3
3a × 4a = 12a2
3a × -2 = -6a
5 × 2a2 = 10a2
5 × 4a = 20a
5 × -2 = -10
Step 2: Combine Like Terms
Now, we need to combine like terms, which means adding or subtracting terms with the same variable and exponent.
6a3 + 12a2 – 6a = 6a3 + 12a2
6a3 + 10a2 – 6a = 6a3 + 10a2
Step 3: Simplify the Expression
The final step is to simplify the expression by combining any remaining like terms.
6a3 + 10a2 = 6a3 + 6a2
6a3 + 6a2 = 6a3 + 6a2
The Final Answer
The product of 3a+5 and 2a2+4a-2 is:
6a3 + 6a2
Key Points to Remember
- When multiplying polynomials, we need to multiply each term in the first polynomial by each term in the second polynomial.
- We need to combine like terms, which means adding or subtracting terms with the same variable and exponent.
- We need to simplify the expression by combining any remaining like terms.
Example Use Cases
- When multiplying two polynomials, we can use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.
- We can also use the FOIL method to multiply two binomials.
Table: Multiplying Polynomials
| 3a | 5 | |
|---|---|---|
| 2a2 | 6a3 | 10a2 |
| 4a | 12a2 | 20a |
| -2 | -6a | -10 |
| 2a2+4a-2 | |
|---|---|
| 3a | 6a3+6a2 |
| 5 | 10a2-10a |
Conclusion
The product of 3a+5 and 2a2+4a-2 is 6a3 + 6a2. This is a simple example of multiplying two polynomials using the distributive property and combining like terms. By following these steps, we can simplify the expression and find the final answer.