maths urgent help P1 w-10 paper 11

[Mortal9090]

P1 w-10 paper 11 question 2

In the expansion of (1 + ax)^6, where a is a constant, the coefficient of x is −30. Find the coefficient
of x^3

please help mark scheme answer doesnt make sense et all? thanks!

 

[Saturation]

First expand (1 + ax)^6 , until you get to "X" :

6C0*1^6* (ax)^0 + 6C1* 1^5 * (ax)^1 + .... =
1 + 6ax + .... (we don't need to continue expanding cause we already got to the term with "X")

So it says the coefficient of "X" = 30

Therefore,
6a = -30
a= -5

Now it becomes:

(1 -5x)^6

Find the coefficient of X^3, so now just expand it like a normal binomial therom question and find the coefficient!'

 

[Mortal9090]

oh that was a killer!! thank you so much!