(x+y)3-(x-y)3 Can Be Factorized As

Jasonbradley

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Jun 17, 2024

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Factoring (x+y)³ - (x-y)³

The expression (x+y)³ - (x-y)³ can be factored using the difference of cubes formula. This formula states that:

a³ - b³ = (a - b)(a² + ab + b²)

Let's break down the steps:

1. Identify a and b: In our expression, a = (x + y) and b = (x - y).

2. Apply the difference of cubes formula: Substitute a and b into the formula: (x + y)³ - (x - y)³ = [(x + y) - (x - y)][(x + y)² + (x + y)(x - y) + (x - y)²]

3. Simplify the expression:

   • (x + y) - (x - y) = 2y
   • (x + y)² = x² + 2xy + y²
   • (x + y)(x - y) = x² - y²
   • (x - y)² = x² - 2xy + y²

   Substituting these back into the equation: 2y [x² + 2xy + y² + x² - y² + x² - 2xy + y²]

4. Combine like terms: 2y [3x² + y²]

Therefore, the factored form of (x+y)³ - (x-y)³ is 2y(3x² + y²).