Question

Write the following cube in expanded form: ${\left(2A-3B\right)}^3$

Answer 1

Expand ${\left(2A-3B\right)}^3$:

Use the formula, ${\left(X-Y\right)}^3=X^3-Y^3-3X^{2}Y+3X{Y}^2$

Put, $X=2A,Y=3B$.

$\begin{array}{rcl}{\left(2A-3B\right)}^3& =& {\left(2A\right)}^3-{\left(3B\right)}^3-3{\left(2A\right)}^2\left(3B\right)+3\left(2A\right){\left(3B\right)}^2\\ & \Rightarrow & {\left(2A-3B\right)}^3=8A^3-27B^3-36A^{2}B+54A{B}^2\end{array}$

Hence, the expanded form of ${\left(2A-3B\right)}^3$ is $8A^3-27B^3-36A^{2}B+54A{B}^2$.