# NCERT Solutions Class 8 Mathematics Solutions for Exercise 14.2 in Chapter 14 - Factorisation

Question 9 Exercise 14.2

Factorise:

25 a^{2}-4 b^{2}+28 b c-49 c^{2}

Answer:

Solution:

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Here we will be using the following two identities :

a2-2ab+b2= (a-b)2 and

a2-b2= (a+b)(a-b)

\begin{aligned} &=25 a^{2}-\left(4 b^{2}-28 b c+49 c^{2}\right)\\ &=(5 a)^{2}-\left\{(2 b)^{2}-2(2 b)(7 c)+(7 c)^{2}\right\}\\ &=(5 a)^{2}-(2 b-7 c)^{2}\\ &\text { Using Identity: } x^{2}-y^{2}=(x+y)(x-y) \text { , we have }\\ &=(5 a+2 b-7 c)(5 a-2 b-7 c) \end{aligned}

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