Question

The coefficient of x in (x + 3)³ is
(a) 1
(b) 9
(c) 18
(d) 27

Answer 1

$$\begin{gathered} {\left(x+3\right)}^3 \\ ={\left(x\right)}^3+{\left(3\right)}^3+3\left(x\right)\left(3\right)\left(x+3\right)\left(\mathrm{Using}\mathrm{the}\mathrm{identity}:{\left(a+b\right)}^3=a^3+b^3+3ab\left(a+b\right)\right) \\ =x^3+27+9x\left(x+3\right) \\ =x^3+27+9x^2+27x \\ =x^3+9x^2+27x+27 \\ \mathrm{Thus},\mathrm{the}\mathrm{coefficient}\mathrm{of}x\mathrm{is}27. \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{d}\right). \end{gathered}$$