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Subject:  Precalculus

Expand (3x + 2)⁴

Apply the binomial theorem with both coefficients larger than 1.

Answer 81x⁴ + 216x³ + 216x² + 96x + 16

Solution

  1. Binomial (3x + 2)⁴
  2. Term k = 0 C(4,0)·(3x)⁴·(2)⁰ = 81x⁴
  3. Term k = 1 C(4,1)·(3x)³·(2)¹ = 216x³
  4. Term k = 2 C(4,2)·(3x)²·(2)² = 216x²
  5. Term k = 3 C(4,3)·(3x)¹·(2)³ = 96x
  6. Term k = 4 C(4,4)·(3x)⁰·(2)⁴ = 16
  7. Expansion 81x⁴ + 216x³ + 216x² + 96x + 16

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