Factorise the following by using suitable identities.$(a-b)^2- (b-c)^2$

Given:

$(a-b)^2- (b-c)^2$

To do:

We have to factorise the given expression using suitable identities.

Solution:

We know that,

$x^2-y^2=(x-y)(x+y)$

Therefore,

$(a-b)^2- (b-c)^2=[(a-b)-(b-c)][(a-b)+(b-c)]$

$=(a-b-b+c)(a-b+b-c)$

$=(a-2b+c)(a-c)$

Therefore, $(a-b)^2- (b-c)^2=(a-2b+c)(a-c)$.

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Updated on: 10-Oct-2022

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