Question

find the coefficient of X in the expansion of (X + 3) cube

Answer 1

(x + 3)^3

= x^3 + (3)^3 + 3(x) (3) ( x +3)

= x^3 + 27 + 9x ( x + 3)

= x^3 + 27 + 9x^2 + 27x

= x^3 + 9x^2 + 27x + 27

Coficient of x is 27

Answer 2

Suppose (r+1)th term contains x¹ in the bionomial expansion of (x+3)³

Now,

$T_{r+1} = \ ^{3}C_r \ x^{3-r} \ 3^{r} \ \\ \\ but, \\ \\ 3- r = 1 \\ \\ r = 2 \\ \\ So, \\ \\ T_{r+1} = \ ^{3}C_r \ x^{3-r} \ 3^{r} \\ \\ T_{2+1} = \ ^{3}C_2 \ x^{3-2} \ 3^{2} \\ \\ T_3 = 3* x * 9 \\ \\ = 27x \\ \\ \textbf{Coefficient of x = 27}$