Expand using suitable identities
$(2 a - 3 b)^{3}$

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Solution

We need to expand $(2 a - 3 b)^{3}$
We know suitable identity is $(x - y)^{3} = x^{3} - 3 x^{2} y + 3 x y^{2} + y^{3}$
Here $x = 2 a$ and $y = 3 b$
Therefore, value of $(2 a - 3 b)^{3}$ is
$= (2 a)^{3} - 3 (2 a)^{2} (3 b) + 3 (2 a) (3 b)^{2} - (3 b)^{3}$
$= 8 a^{3} - 36 a^{2} b + 54 a b^{2} - 27 b^{3}$

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Question 85 (ix)

Expand the following, using suitable identities.

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

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Expand the following, using suitable identities.

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

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