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1. The problem statement, all variables and given/known data

A) Three consecutive coefficients in the expansion of (1+x)^n are in the ratio 6:14:21. Find the value of n.

B) Find the independent term in the [2x + 1 - 1/(2x^2)]^6 (independent term is x^0)

C) In the expansion of (1 + ax)^n the first term is 1, the second term is 24x, and the third term is 252x^2. Find the values of a and n

D) In the expansion of (x + a)^3(x - b)^6, the coefficient of x^7 is -9 and there is no x^8 term. Find a and b.

2. Relevant equations

3. The attempt at a solution

A) I realized that the coefficients are n C r, n C (r+1), and n C (r+2), and that they are in ratio of 6:14:21. However I am not sure how to find n after this step.

B) I tried substituting a variable y { let y = 2x - 1/(2x^2) } to form (y + 1)^6. I could expand it all out and test each term using the general term of binomial expansion, but that would be very tedious. I am wondering if there is a better solution

C) I simplified C) to (a)(n C 1) = 24 and (a^2)(n C 2) = 252. Now I'm stuck on what to do next

D) I've simplified it to 5b^2 -6ab + a^2 = -3 and -2b^2 +a = 0. I'm not sure how to proceed from this.

Any help is appreciated :)

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# Homework Help: Bionomial Expansions help

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