Question

Write cubes in expanded form${[\frac{3}{2}x+1]}^3$

Answer 1

Using\quad ${(a+b)}^3=a^3+b^3+3ab(a+b)$

$a=\frac{3}{2}x,b=1$

${[\frac{3}{2}x+1]}^3={\left[\frac{3}{2}x\right]}^3+1^3+3\left[\frac{3}{2}x\right]\left[1\right][\frac{3}{2}x+1]$

$=\frac{27}{8}{x}^3+1+\frac{9}{2}[\frac{3}{2}x+1]$

$=\frac{27}{8}{x}^3+1+\frac{9}{2}\left[\frac{3}{2}x\right]+\frac{9}{2}x\left[1\right]$

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