Question

Use the formula to expand the following:

(7) ${\left(6m-\frac{1}{3}\right)}^3$

Answer 1

We know that (x − y)³ = x³ − 3x²y + 3xy² − y³.
Comparing ${\left(6m-\frac{1}{3}\right)}^3$ with (x − y)³, we get:
x = 6m and y = $\frac{1}{3}$
Substituting these in the above formula:

$$\begin{gathered} {\left(6m-\frac{1}{3}\right)}^3={\left(6m\right)}^3-3\times {\left(6m\right)}^2\times \frac{1}{3}+3\times 6m\times {\left(\frac{1}{3}\right)}^2-{\left(\frac{1}{3}\right)}^3 \\ =216m^3-36m^2+2m-\frac{1}{27} \end{gathered}$$