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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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