Question

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

Answer 1

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

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

Put, $A=2X,B=1$.

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

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