# Find the Following Product: ( 3 X − 2 X 2 ) ( 9 X 2 + 4 X 4 − 6 X ) - Mathematics

Find the following product:

$\left( \frac{3}{x} - 2 x^2 \right) \left( \frac{9}{x^2} + 4 x^4 - 6x \right)$

#### Solution

Given$\left( \frac{3}{x} - 2 x^2 \right) \left( \frac{9}{x^2} + 4 x^4 - 6x \right)$

We shall use the identity  (a-b)(a^2 + ab + b^2) = a^3 - b^3

We can rearrange the $\left( \frac{3}{x} - 2 x^2 \right) \left( \frac{9}{x^2} + 4 x^4 - 6x \right)$ as

$\left( \frac{3}{x} - 2 x^2 \right)\left( \left( \frac{3}{x} \right)^2 + \left( 2 x^2 \right)^2 - \left( \frac{3}{x} \right)\left( 2 x^2 \right) \right)$

$= \left( \frac{3}{x} \right)^3 - \left( 2 x^2 \right)^3$

$= \left( \frac{3}{x} \right)\left( \frac{3}{x} \right)\left( \frac{3}{x} \right) - \left( 2 x^2 \right)\left( 2 x^2 \right)\left( 2 x^2 \right)$

$= \frac{27}{x^3} - 8 x^6$

Hence the Product value of $\left( \frac{3}{x} - 2 x^2 \right) \left( \frac{9}{x^2} + 4 x^4 - 6x \right)$ is 27/x^3 - 8x^6.

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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Exercise 4.4 | Q 1.08 | Page 24