Question

(3a/5 + 2b/3) (3a/5-2b/3) =?
(A) 3a²/5-2b²/3
(B) 9a²/5-4b²/9
(C) 9a²/25-4b²/9
(D) 9a²/25-4b²/3
​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\displaystyle \sf{ \bigg( \frac{3a}{5} + \frac{2b}{3} \bigg)\bigg( \frac{3a}{5} - \frac{2b}{3} \bigg)}$

(A) 3a²/5-2b²/3

(B) 9a²/5-4b²/9

(C) 9a²/25-4b²/9

(D) 9a²/25-4b²/3

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

$\sf{ {a}^{2} - {b}^{2} = (a + b)(a - b) }$

EVALUATION

$\displaystyle \sf{ \bigg( \frac{3a}{5} + \frac{2b}{3} \bigg)\bigg( \frac{3a}{5} - \frac{2b}{3} \bigg)}$

$\displaystyle \sf{ = {\bigg( \frac{3a}{5} \bigg)}^{2} - {\bigg( \frac{2b}{3} \bigg)}^{2} } \: \: (by \: above \: identity)$

$\displaystyle \sf{ = \frac{9 {a}^{2} }{25} - \frac{4 {b}^{2} }{9} }$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{ (c) \: \: \frac{9 {a}^{2} }{25} - \frac{4 {b}^{2} }{9} }$

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Answer 2

Step-by-step explanation:

9a²/25 -4b²/9 (ans by *Ritesh Verma*