What is the result of (x + 1)² - (x - 1)²?

What is the result of (x + 1)² - (x - 1)²?

Step 1: Start with the expression (x + 1)² - (x - 1)².
Step 2: Expand (x + 1)² using the formula (a + b)² = a² + 2ab + b². Here, a = x and b = 1.
Step 3: (x + 1)² = x² + 2x + 1.
Step 4: Expand (x - 1)² using the same formula. Here, a = x and b = -1.
Step 5: (x - 1)² = x² - 2x + 1.
Step 6: Now substitute the expanded forms back into the original expression: (x² + 2x + 1) - (x² - 2x + 1).
Step 7: Distribute the negative sign in front of (x² - 2x + 1): (x² + 2x + 1) - x² + 2x - 1.
Step 8: Combine like terms: x² - x² + 2x + 2x + 1 - 1.
Step 9: This simplifies to 4x.

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