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# Binomial Expansion watch

1. Hi, can someone help me do this question

The coefficient of x³ in the expansion of (2 + x)(3 - ax)^4 is 30.
Find the values of the constant a.

I can do the question, but i done it in some extremly long way. Can someone do this for me?

Thanks
2. How long? Maybe you did it the best way...
Expand (3-ax)4 as you normally would, and multiply the whole thing by (2+x). Obviously, you can save time by only working out which terms will be the x3 terms (if you're confident enough to do so).
Then just equate the x3 terms to 30, and solve for a.
3. Yep, thats what i done. However you end up with something like:

24a³ - 54a² + 30 = 0

Then i used the factor thearom to factorise it and solve for a.
But thats long!!
4. 24a³ - 54a² + 30 = 0

4a³ - 9a² + 5 = 0

(4a - 5)(a - 1) = 0
5. (Original post by seankhn)
(4a - 5)(a - 1) = 0
You cant do that. When you expand that you get 4a². I think the factor thearom is the only way for that question.
6. cant u let a^2 = k then u will have ur standard quadratic ,solve for k and sub a back in ?
7. (a-1)(a-1.9058)(a+0.655)

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