(a). expand(1+3X)^4and (2-x)^5respectively in ascending power of x as far as the term in x^s.
(B).Hence expand(1+3x)^4(2-x)^5 as far as the term in x^2.
How to hence?
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M1-Binomial theorem
2011-10-11 5:09 am
回答 (2)
2011-10-11 5:31 am
✔ 最佳答案
a)(1 + 3x)⁴= 1 + 4(3x) + 4C2 * 9x² + 4C3 * 27x³ + 81x⁴ = 1 + 12x + 54x² + 108x³ + 81x⁴ (2 - x)⁵= 2⁵ + 5(2)⁴(- x) + 5C2 * 2³ (- x)² + 5C3 * 2² (- x)³ + 5C4 * 2 (- x)⁴+ (- x)⁵ = 32 - 80x + 80x² - 40x³ + 10x⁴- x⁵b)(1 + 3x)⁴(2 - x)⁵= (1 + 12x + 54x² + ...) (32 - 80x + 80x² - ...)= (32 - 80x + 80x²) + (12x)(32 - 80x + ...) + 54x²(32 - ...) + ...= 32 - 80x + 80x² + 384x - 960x² + 1728x² + ...= 32 + 304x + 848x² + ...
2011-10-11 5:34 am
b) 32 - 464x + 2768x^2 - 8776x^3 + 16042x^4 - 17401x^5 + 11352x^6 - 4374x^7 + 918x^8 - 81x^9
收錄日期: 2021-04-21 22:22:29
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