Question

Evaluate the following ${(\frac{3}{2}x+1)}^3-\frac{{27x}^2}{4}-\frac{9x}{2}$

Answer 1

${(\frac{3x}{2}+1)}^3-\frac{27x^2}{4}-\frac{9x}{2}$

$={\left(\frac{3x}{2}\right)}^3+1+3\times \frac{3x}{2}\times 1(\frac{3x}{2}+1)-\frac{27x^2}{4}-\frac{9x}{2}$

$=\frac{27x^3}{8}+1+\frac{27x^2}{4}+\frac{9x}{2}-\frac{27x^2}{4}-\frac{9x}{2}$

$=\frac{27x^3}{8}+1$