Binomial Theorem/Examples/Cube of Sum/Corollary

Corollary to Cube of Sum

$\paren {x + 1}^3 = x^3 + 3 x^2 + 3 x + 1$


Proof

Follows directly from the Cube of Sum:

$\paren {x + y}^3 = x^3 + 3 x^2 y + 3 x y^2 + y^3$

setting $y = 1$.

$\blacksquare$


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $24$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24$
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