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(n^2-3n+1)(2n+3)=

2 min read Jun 16, 2024
(n^2-3n+1)(2n+3)=

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.

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