The correct option is A 6a^2 5a/b 6/b^2 3a+2b2a 3b = (3a)(2a) + (2/b)(2a) (3/b)(3a) (2/b)(3/b) = 6a^2 + (4/b 9/b)a 6/b^2 = 6a^2 + ( 5/b)a 6/b^2 ...

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Introduction to Algebraic Identities

Expand 3a+2b2...

Question

Expand $(3 a + \frac{2}{b}) (2 a - \frac{3}{b})$

6 a^{2} - \frac{5 a}{b} - \frac{6}{b^{2}}

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6 a^{2} + \frac{5 a}{b} - \frac{6}{b^{2}}

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6 a^{2} + \frac{5 a}{b} + \frac{6}{b^{2}}

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6 a^{2} - \frac{5 a}{b} + \frac{6}{b^{2}}

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Solution

The correct option is A $6 a^{2} - \frac{5 a}{b} - \frac{6}{b^{2}}$
$(3 a + \frac{2}{b}) (2 a - \frac{3}{b})$
= $(3 a) (2 a) + (\frac{2}{b}) (2 a) - (\frac{3}{b}) (3 a) - (\frac{2}{b}) (\frac{3}{b})$

= $6 a^{2} + (\frac{4}{b} - \frac{9}{b}) a - \frac{6}{b^{2}}$

= $6 a^{2} + (\frac{- 5}{b}) a - \frac{6}{b^{2}}$

= $6 a^{2} - \frac{5 a}{b} - \frac{6}{b^{2}}$

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