Question

State True or False.

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

• A. True
• B. False

Answer 1

The correct option is A True

Using, $(a+b{)}^3=a^3+b^3+3ab(a+b)$
$(\frac{3}{2}x+1{)}^3=(\frac{3}{2}x{)}^3+(1{)}^3+3(\frac{3}{2}x\left)\right(1\left)\right(\frac{3}{2}x+1)$
$=\frac{27}{8}{x}^3+1+\frac{9}{2}x(\frac{3}{2}x+1)$
$=\frac{27}{8}{x}^3+1+\frac{27}{4}{x}^2+\frac{9}{2}x$
$=\frac{27}{8}{x}^3+\frac{27}{4}{x}^2+\frac{9}{2}x+1$