Engineering Board Exam Reviewer · Binomial Theorem · hard

Find the coefficient of x3 in the expansion of (1+x)4(1-x)2.

1. 4
2. -4
3. -2
4. 6

Answer

B. -4

Solution

(1+x)4(1-x)2=(1+x)2≤ft(1-x2 )2=(1+2x+x2)(1-2x2+x4). The x3 terms come from 2x·(-2x2)=-4x3 only, so the coefficient is -4.

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1. The coefficients of the 2nd, 3rd, and 4th terms in the expansion of (1+x)n are in arithmetic progression. Find n (with n≥3).
2. Using the first three terms of the binomial expansion, approximate (1.02)10.
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4. Find the term independent of x in the expansion of ≤ft(2x2- 1x )9.
5. Find the constant term in the expansion of ≤ft(x+ 1x )10.
6. Find the coefficient of x5 in the expansion of (2x-1)8.
7. Find the 4th term in the expansion of (x+y)6.

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