Question

Write the following cubes in expanded form: ${\left(2x+1\right)}^3$

Answer 1

Expand ${\left(2x+1\right)}^3$:

Use the formula ${\left(u+v\right)}^3=u^3+v^3+3u^{2}v+3u{v}^2$.

Put $u=2x,v=1$.

$\begin{array}{rcl}{\left(2x+1\right)}^3& =& {\left(2x\right)}^3+1^3+3{\left(2x\right)}^2\left(1\right)+3\left(2x\right){\left(1\right)}^2\\ & \Rightarrow & {\left(2x+1\right)}^3=8x^3+1+12x^2+6x\end{array}$

Hence, expanded form of ${\left(2x+1\right)}^3$ is $8x^3+1+12x^2+6x$.