WAEC Further Mathematics 2022 Theory — Question 11
Question 11 of 15 from the West African Examinations Council (WAEC) Further Mathematics 2022 Theory paper, with the correct answer and a full explanation.
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11(a) Find the binomial expansion of (1+2x)⁷ and (1−2x)⁷. (b) Using the result in (a), find, correct to three decimal places, the value of (1.2)⁷ − (0.8)⁷.
Model answer
(a) (1+2x)⁷ = 1+14x+84x²+280x³+560x⁴+672x⁵+448x⁶+128x⁷ (1−2x)⁷ = 1−14x+84x²−280x³+560x⁴−672x⁵+448x⁶−128x⁷ (b) Setting x=0.1 (so 1+2x=1.2, 1−2x=0.8): (1.2)⁷−(0.8)⁷ = 2(14x+280x³+672x⁵+128x⁷) = 2(1.4+0.28+0.00672+0.0000128) ≈ 3.373 (to 3 d.p.).
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