Additional Mathematics – Series | e-Consult
Series (1 questions)
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Answer: Expanding both powers and subtracting, only the odd‑power terms survive:
(1 + x)6 − (1 − x)6 = 2[C(6,1)x + C(6,3)x3 + C(6,5)x5]
Evaluating the binomial coefficients:
- C(6,1)=6
- C(6,3)=20
- C(6,5)=6
Thus the simplified expression is:
12x + 40x3 + 12x5.