Question

Factorise 64/125 p³ - 8 - 96/25 p² + 48/5 p

Answer 1

Dear student

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