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Expanding and Simplifying the Expression: (n^2-3n+1)(2n+3)
This article will guide you through the process of expanding and simplifying the given expression: (n^2-3n+1)(2n+3).
Step 1: Expanding the Expression
We can expand the expression by applying the distributive property (also known as FOIL - First, Outer, Inner, Last):
- First: Multiply the first terms of each binomial: n² * 2n = 2n³
- Outer: Multiply the outer terms of the binomials: n² * 3 = 3n²
- Inner: Multiply the inner terms of the binomials: -3n * 2n = -6n²
- Last: Multiply the last terms of the binomials: -3n * 3 = -9n
Now, we multiply the monomial (2n + 3) by the constant term:
- 1 * 2n = 2n
- 1 * 3 = 3
Step 2: Combining Like Terms
We have the following terms after expansion:
2n³ + 3n² - 6n² - 9n + 2n + 3
Now, combine the terms with the same powers of 'n':
- 2n³
- (3n² - 6n²) = -3n²
- (-9n + 2n) = -7n
- 3
Step 3: Simplified Expression
Combining all the terms, we get the simplified expression:
2n³ - 3n² - 7n + 3
Therefore, the expanded and simplified form of the expression (n²-3n+1)(2n+3) is 2n³ - 3n² - 7n + 3.