Binomial expansion
(a+b)n = Σ nCr an-rbr. Y13 extends to rational n.
Y12: (a+b)n for n a positive integer. Y13: rational/negative n via (1+x)n series for |x| < 1.
Worked examples
(1 + x)4 = 1 + 4x + 6x² + 4x³ + x4.
(2 + 3x)5: term in x² is C(5,2) × 2³ × (3x)² = 720x².
(1 + x)1/2 ≈ 1 + x/2 − x²/8 + ... for small x.
Frequently asked questions
nCr notation?
C(n, r) = n!/(r!(n-r)!). Casio button: nCr.
Range of validity (rational n)?
Series converges for |x| < 1. Always state.