# NCERT Solutions Class 8 Mathematics Solutions for Exercise 14.3 in Chapter 14 - Factorisation

Question 9 Exercise 14.3

Factorize the expressions and divide them as directed:

12 x y\left(9 x^{2}-16 y^{2}\right) \div 4 x y(3 x+4 y)

Solution:

Factoring is the process of breaking down one object (such as a number, or polynomial) into a product of another object, or factors, which when multiplied together produce the original object.

\begin{aligned} &\text { Factorize } 9 x^{2}-16 y^{2}, \text { we have }\\ &9 x^{2}-16 y^{2}=(3 x)^{2}-(4 y)^{2}=(3 x+4 y)(3 x-4 y) \text { using identity: } p^{2}-q^{2}=(p-q)(p+q)\\ &\text { Now, } 12 x y\left(9 x^{2}-16 y^{2}\right) \div 4 x y(3 x+4 y)=12 x y(3 x+4 y)(3 x-4 y) / 4 x y(3 x+4 y)=3(3 x-4 y) \end{aligned}

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