Question

The coefficient of x in the expansion of (x + 5)³ is

(a) 1
(b) 15
(c) 45
(d) 75

Answer 1

(d) 75

${\left(x+5\right)}^3=x^3+5^3+\left(3\times x\times 5\right)\left(x+5\right)$
$$\begin{gathered} =x^3+125+15x\times \left(x+5\right) \\ =x^3+125+15x^2+75x \end{gathered}$$

Hence, the coefficient of x is 75.