(x+1)^2-(x-1)^2-3(x+1)(x-1)

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

Simplifying the Expression (x+1)² - (x-1)² - 3(x+1)(x-1)

This article aims to simplify the given algebraic expression: (x+1)² - (x-1)² - 3(x+1)(x-1).

Understanding the Expression

The expression involves squaring binomials and multiplying them. We can use the following algebraic identities to simplify the expression:

  • (a + b)² = a² + 2ab + b²
  • (a - b)² = a² - 2ab + b²
  • (a + b)(a - b) = a² - b²

Simplifying the Expression

  1. Expand the squares:

    • (x+1)² = x² + 2x + 1
    • (x-1)² = x² - 2x + 1
  2. Substitute the expanded forms into the original expression:

    • (x² + 2x + 1) - (x² - 2x + 1) - 3(x+1)(x-1)
  3. Expand the last term using the difference of squares identity:

    • (x² + 2x + 1) - (x² - 2x + 1) - 3(x² - 1)
  4. Distribute the negative sign and the constant 3:

    • x² + 2x + 1 - x² + 2x - 1 - 3x² + 3
  5. Combine like terms:

    • (x² - x² - 3x²) + (2x + 2x) + (1 - 1 + 3)
  6. Simplify:

    • -3x² + 4x + 3

Conclusion

The simplified form of the expression (x+1)² - (x-1)² - 3(x+1)(x-1) is -3x² + 4x + 3. By using algebraic identities and carefully combining terms, we have successfully simplified the given expression.

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