Expanding the given expression:The given expression is (2x 2/x)^3.Use identity (a b)^3=a^3 b^3 3ab(a b) to expand.Compare given expression with the identity we ...

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Standard XII

Mathematics

Identity Function

Expand 2x-2/x...

Question

Expand ${(2 x - \frac{2}{x})}^{3}$ .

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Solution

Expanding the given expression:
The given expression is ${(2 x - \frac{2}{x})}^{3}$ .
Use identity $(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$ to expand.
Compare given expression with the identity we have, $a = 2 x, b = \frac{2}{x}$ .
Substitute values in identity we have:
${(2 x - \frac{2}{x})}^{3} = {(2 x)}^{3} - {(\frac{2}{x})}^{3} - 3 (2 x) (\frac{2}{x}) (2 x - \frac{2}{x}) = 8 x^{3} - \frac{8}{x^{3}} - 12 (2 x - \frac{2}{x}) = 8 x^{3} - \frac{8}{x^{3}} - 24 x + \frac{24}{x}$
Hence, the expression, ${(2 x - \frac{2}{x})}^{3} = 8 x^{3} - \frac{8}{x^{3}} - 24 x + \frac{24}{x}$ .

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Expand 2x-2x3.

Expand ${(2 x - \frac{2}{x})}^{3}$ .