Question

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

Answer 1

Expand ${\left(2a-3b\right)}^3$:

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

Put $u=2a,v=3b$.

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

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