Question

Expand using identities
(2/3x-3/2y)^2

Answer 1

$\: \: \: \: \: \: \large \rm { \bigg( \frac{2}{3x} - \frac{3}{2y} \bigg)}^{2} \\ \\ \to \rm {\bigg(\frac{2}{3x}\bigg)}^{2} + {\bigg( \frac{3}{2y} \bigg)}^{2} + 2{\bigg( \frac{2}{3x} \bigg)}{\bigg( \frac{3}{2y} \bigg)} \\ \\ \to \boxed{\rm\frac{4}{ {9x}^{2} } + \frac{9}{ {4y}^{2} } + \frac{2}{xy} \: \: \: \: \: }\\ \\ \underline{ \: \: \longrightarrow {\rm\frac{4 {x}^{ ( - 2)} }{ {9}^{} } + \frac{9 {y}^{( - 2)} }{ {4}^{} } + {2 {(xy)}^{ - 1} }{} \: \: \: \: \:}}$