(2n%2B3).jpeg "(n2−3n+1)(2n+3)")
Expanding and Simplifying (n²-3n+1)(2n+3)
This article will guide you through the process of expanding and simplifying the expression (n²-3n+1)(2n+3).
Expanding the Expression
We can expand this expression using the distributive property. This means we multiply each term in the first set of parentheses by each term in the second set of parentheses.
Step 1: Multiply n² by each term in the second set of parentheses.
- n² * 2n = 2n³
- n² * 3 = 3n²
Step 2: Multiply -3n by each term in the second set of parentheses.
- -3n * 2n = -6n²
- -3n * 3 = -9n
Step 3: Multiply 1 by each term in the second set of parentheses.
- 1 * 2n = 2n
- 1 * 3 = 3
Step 4: Combine all the terms:
(n²-3n+1)(2n+3) = 2n³ + 3n² - 6n² - 9n + 2n + 3
Simplifying the Expression
Now, we can combine the like terms to simplify the expression.
Step 1: Combine the n² terms: 3n² - 6n² = -3n²
Step 2: Combine the n terms: -9n + 2n = -7n
Step 3: Write the final simplified expression:
2n³ - 3n² - 7n + 3
Final Result
Therefore, the expanded and simplified form of (n²-3n+1)(2n+3) is 2n³ - 3n² - 7n + 3.