About Lesson
7.1 Binomial Theorem with Natural Number Power 指数为自然数的二项式定理
[1]
Expand the following binomials :
展开以下的二项式
(a) (x – 3)
(b) (3x + 2y)
(c) (1 – 3x)
(d) (x – 2)(3x + 1)
(e)
Answer:
(a) –
(b) +
(c) –
(d) –
(e) –
[2]
Find in ascending powers of t, the first three terms in the expansions of
以t的升幂方式展开以下各式的首三项
(a)
(b)
Hence find, in terms of , and , the coefficient of in the expansion of (1 + t)(1 – t).
以此求, 以和表示, 在(1 + t)(1 – t)的展开式中的系数.
Answer:
(a) 1 + 5t + 102t + …
(b) 1 – 8t + 282t – …
10 + 28 – 40
[3]
If (1 + 2x + 3x) = a+ ax + a + … + a. calculate
若 (1 + 2x + 3x) = a+ ax + a + … + a求
(a)
(b)
Answer:
(a) 7776
(b) 3904