I have been given this question:
"Find the value of $c$ if, in the expansion of $(cx + 2)^3$, the coefficient of $x$ is $24$"
To solve this question, I have tried using the 'General Term In Binomial Expression' formula as well as using the pascals triangle and expanding the brackets by hand and then adding in the coefficient, but every attempt still has many square's and cubed numbers remaining.
Best Answer
Each term in the binomial expansion is of the form ${3\choose k}(cx)^k2^{3-k}$, and you want the term with $x^1$ in it, so the $k=1$ term. Then you get $3\cdot cx\cdot 2^2=12cx$. So you have $c=2$.