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

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

Expanding and Simplifying the Expression: (n^2 + 2n - 1)(n^2 + n + 2)

This article will explore the process of expanding and simplifying the given expression: (n^2 + 2n - 1)(n^2 + n + 2). We will use the distributive property and combine like terms to achieve the simplified form.

Expanding the Expression

To expand the expression, we will multiply each term in the first set of parentheses by each term in the second set of parentheses. This process is similar to the FOIL method (First, Outer, Inner, Last), but with more terms.

Step 1: Multiply the first term in the first set of parentheses (n²) by each term in the second set of parentheses:

  • n² * n² = n⁴
  • n² * n = n³
  • n² * 2 = 2n²

Step 2: Multiply the second term in the first set of parentheses (2n) by each term in the second set of parentheses:

  • 2n * n² = 2n³
  • 2n * n = 2n²
  • 2n * 2 = 4n

Step 3: Multiply the third term in the first set of parentheses (-1) by each term in the second set of parentheses:

  • -1 * n² = -n²
  • -1 * n = -n
  • -1 * 2 = -2

Combining Like Terms

Now, we have all the terms expanded. The next step is to combine the terms with the same variable and exponent:

  • n⁴
  • n³ + 2n³ = 3n³
  • 2n² + 2n² - n² = 3n²
  • 4n - n = 3n
  • -2

The Simplified Expression

Putting it all together, the simplified form of the expression is:

(n^2 + 2n - 1)(n^2 + n + 2) = n⁴ + 3n³ + 3n² + 3n - 2

This is the final expanded and simplified form of the given expression.

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