Question

evaluate
Q.14. Evaluate the following: ${\left(\frac{3}{2}x+1\right)}^3-\frac{27x^2}{4}-\frac{9x}{2}$

Answer 1

Dear Student,
$$\begin{gathered} {\left(\frac{3}{2}x+1\right)}^3-\frac{27x^2}{4}-\frac{9x}{2} \\ =\frac{27}{8}{x}^3+3\times \frac{9}{4}{x}^2\times 1+3\times \frac{3}{2}x\times 1^2+1^3-\frac{27x^2}{4}-\frac{9x}{2}\left[u\sin g{\left(a+b\right)}^3=a^3+3a^{2}b+3a{b}^2+b^3\right] \\ =\frac{27x^3}{8}+\frac{27x^2}{4}+\frac{9x}{2}+1-\frac{27x^2}{4}-\frac{9x}{2} \\ =\frac{\mathbf{27}{\mathbf{x}}^{\mathbf{3}}}{\mathbf{8}}\mathbf{+}\mathbf{1} \end{gathered}$$
Regards