Q7 of 65 Page 137

Let us factorise the following algebraic expressions:

a2 + b2 – c2 – 2ab

Given, a2 + b2 – c2 – 2ab


⇒ This can be written as a2 – 2ab + b2 – c2


⇒ From the identity II, a2 – 2ab + b2 = (a – b)2


∴ (a – b)2 – c2


⇒ ((a – b) – c)((a – b) + c)


[Since, from the identity III we know that, (x2 – y2) = (x – y)(x + y)]


⇒ (a – b – c)(a – b + c)


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