Find 8x^3-1/8x^3 when 2x-1/2x=p [S.Chand ICSE Class 9 Chapter 3 Exercise 3.1 Expansion and Factorisation Solution ]
$\left(2x – \frac{1}{2x}\right) = p$
$\therefore \left(2x – \frac{1}{2x}\right)^3 = p^3$
$\Rightarrow \left(2{\mathrm{x}}\right)^3 – \left(\frac{1}{2{\mathrm{x}}}\right)^3 – 3.2{\mathrm{x}}\ldotp \frac{1}{2{\mathrm{x}}}\left(2x – \frac{1}{2x}\right) = p^3$
$\Rightarrow \left(2{\mathrm{x}}\right)^3 – \left(\frac{1}{2{\mathrm{x}}}\right)^3 – 3(p) = p^3$
$\Rightarrow \left(2{\mathrm{x}}\right)^3 – \left(\frac{1}{2{\mathrm{x}}}\right)^3 = p^3 + 3p$
$\Rightarrow 8{\mathrm{x}}^3 – \frac{1}{8{\mathrm{x}}^3} = p^3 + 3p$
$\therefore 8{\mathrm{x}}^3 – \frac{1}{8{\mathrm{x}}^3} = p^3 + 3p$