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

Jasonbradley

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Jun 16, 2024

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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.