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Chapter 5 C2 help

'The coefficient of x^2 in the expansion (2+ax)^3 is 54. Find the possible values of the constant a'

So I have expanded it and found that the coefficient in terms of a is 6ax^2 so a would be 9 but the answer is +/- 3, where have I gone wrong?

Reply 1

TheIrrational

Original post by physicshelpme

Remember when you square ax you get

a^2x^2

so your term for

x^2

has coefficient

6a^2

Reply 2

physicshelpme

Another question where I don't know what I've done wrong.

'The coefficient of x^3 in the expansion (2+x)(3-ax)^4 is 30, find the values of the constant a'

This is my working:

1) (1)(3^4) + (4)(3^3)(-ax) + (6)(3^2)(-ax)^2 + (4)(3)(-ax)^3 + (1)(-ax)^4
2) 81 - 108ax + 54(a^2)(x^2) - 12(a^3)(x^3) + (a^4)(x^4)
3) 162 - 216ax + 108(a^2)(x^2) - 24(a^3)(x^3) + 2(a^4)(x^4)
4) 162x - 216a(x^2) + 108(a^2)(x^3) - 24(a^3)(x^4) + 2(a^4)(x^5)
5) 108(a^2)(x^3) = 30x^3
6) 108(a^2) = 30
7) (a^2) = 5/18
8) a = +/- root 5/18

Where have I gone wrong? Thank you