(a+b)^3-8b^3

Jasonbradley

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Jun 16, 2024

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Factoring (a + b)³ - 8b³

This expression can be factored using the difference of cubes formula.

The difference of cubes formula is:

a³ - b³ = (a - b)(a² + ab + b²)

Let's apply this to our expression:

1. Recognize the cubes:

   • (a + b)³ is the cube of (a + b)
   • 8b³ is the cube of 2b

2. Substitute into the formula:

   • Let a = (a + b)
   • Let b = 2b

   Now we can rewrite the expression:

   (a + b)³ - 8b³ = [(a + b) - 2b][(a + b)² + (a + b)(2b) + (2b)²]

3. Simplify:

   • [(a + b) - 2b] = a - b
   • [(a + b)² + (a + b)(2b) + (2b)²] = a² + 2ab + b² + 2ab + 2b² + 4b² = a² + 4ab + 7b²

4. Final factored expression:

   (a + b)³ - 8b³ = (a - b)(a² + 4ab + 7b²)

Therefore, the factored form of (a + b)³ - 8b³ is (a - b)(a² + 4ab + 7b²).