Question

(x-2/3y)^3 expand using suitable identity ​

Answer 1

Step-by-step explanation:

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we know that

(a-b)³= a³-3a²b+3ab²-b³

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$= {(x - \frac{2}{3y} )}^{3}$

$= {x}^{3} - 3 {(x})^{2} ( \frac{2}{3y} ) + 3(x) {( \frac{2}{3y} )}^{2} - {( \frac{2}{3y} })^{3}$

$= {x}^{3} - \frac{ {2x}^{2} }{y} + \frac{12x}{ {9y}^{2} } - \frac{8}{ {27y}^{3} }$

$= {x}^{3} - \frac{2 {x}^{2} }{y} + \frac{4}{ {3y}^{2} } - \frac{8}{ {27y}^{3} }$

$\bf = {x}^{3} - \frac{2 {x}^{2} }{y} + \frac{ {4y}^{2} }{3} - \frac{ {8y}^{3} }{27}$