Question

Expand ${\left(\frac{4}{5}x-2\right)}^3$.

Answer 1

Expanding the given expression:

The given expression is ${\left(\frac{4}{5}x-2\right)}^3.$

Use identity, ${\left(a-b\right)}^3=a^3-b^3-3ab\left(a-b\right)$ to expand the expression.

Comparing expression with identity we have, $a=\frac{4x}{5},b=2$.

Substituting values in identity we get:

$$\begin{gathered} {\left(\frac{4x}{5}-2\right)}^3={\left(\frac{4x}{5}\right)}^3-{\left(2\right)}^3-3\left(\frac{4x}{5}\right)\left(2\right)\left(\frac{4x}{5}-2\right) \\ =\frac{64x^3}{125}-8-\frac{24x}{5}\left(\frac{4x}{5}-2\right) \\ =\frac{64x^3}{125}-8-\frac{96x^2}{25}+\frac{48x}{5} \end{gathered}$$

Hence the expression, ${\left(\frac{4x}{5}-2\right)}^3=\frac{64x^3}{125}-8-\frac{96x^2}{25}+\frac{48x}{5}$.