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Subject:  Precalculus

Expand (x + 1)⁵

Apply the binomial theorem with whole-number exponent 5.

Answer x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

Solution

  1. Binomial (1x + 1)⁵
  2. Term k = 0 C(5,0)·(1x)⁵·(1)⁰ = 1x⁵
  3. Term k = 1 C(5,1)·(1x)⁴·(1)¹ = 5x⁴
  4. Term k = 2 C(5,2)·(1x)³·(1)² = 10x³
  5. Term k = 3 C(5,3)·(1x)²·(1)³ = 10x²
  6. Term k = 4 C(5,4)·(1x)¹·(1)⁴ = 5x
  7. Term k = 5 C(5,5)·(1x)⁰·(1)⁵ = 1
  8. Expansion x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

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