(2n%2B1).jpeg "(3n^2+2n-5)(2n+1)")
Expanding the Expression (3n² + 2n - 5)(2n + 1)
This article will guide you through the steps of expanding the expression (3n² + 2n - 5)(2n + 1). This type of problem involves multiplying two binomials, a fundamental skill in algebra.
1. Understanding the Process
Expanding this expression means multiplying each term in the first binomial by each term in the second binomial. This is often referred to as the FOIL method:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
2. Applying the FOIL Method
Step 1: First terms: (3n²) * (2n) = 6n³
Step 2: Outer terms: (3n²) * (1) = 3n²
Step 3: Inner terms: (2n) * (2n) = 4n²
Step 4: Last terms: (2n) * (1) = 2n
Step 5: Last terms: (-5) * (2n) = -10n
Step 6: Last terms: (-5) * (1) = -5
3. Combining Like Terms
Now we have: 6n³ + 3n² + 4n² + 2n - 10n - 5
Combining like terms, we get: 6n³ + 7n² - 8n - 5
Conclusion
Therefore, the expanded form of the expression (3n² + 2n - 5)(2n + 1) is 6n³ + 7n² - 8n - 5. Remember, understanding the FOIL method is essential for effectively expanding binomial expressions in algebra.