Question

use the standard formula
(3a/2b-2b /3a) ^2
Plss answer this question
Lesson ALGEBRA EXPANSION
CLASS 9​

Answer 1

using Algebric identifies :-

• (a - b)² = a² + b² - 2ab

solution :-

$:\implies\sf \: \frac{3a}{2b} - \frac{2b}{3a}^{2} \\ \\ \\ :\implies\sf \: ( \frac{3a}{2b})^{2} + (\frac{2b}{3a})^{2} - 2 \times \frac{3a}{2b} \\ \\ \\ :\implies\sf \: \frac{9a^{2} }{4b^{2} } + \frac{4b^{2} }{9a^{2} } \\ \\ \\ :\implies\sf \: 2$

learn more about algebric identities :-

$\boxed{\begin{array}{c} \\ \\\:\underline{{\rm{S}{ome\:important\:algebric\:identities\:::}}} \\\\ \green{\bigstar}\:\rm \red{ (A+B)^{2} = A^{2} + 2AB + B^{2}} \\\\ \red{\bigstar}\rm\: \green{(A-B)^{2} = A^{2} - 2AB + B^{2}} \\\\ \orange{\bigstar}\rm\: \blue{A^{2} - B^{2} = (A+B)(A-B)}\\\\ \blue{\bigstar}\rm\: \orange{(A+B)^{2} = (A-B)^{2} + 4AB}\\\\ \pink{\bigstar}\rm\: \purple{(A-B)^{2} = (A+B)^{2} - 4AB}\\\\ \purple{\bigstar} \rm\: \pink{(A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}}\\\\ \gray{\bigstar}\rm\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\ \bigstar\rm\: \gray{A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})} \\\\ \end{array}}$

_____________________________