Q66 of 128 Page 224

State whether the statements are true (T) or false (F).

The factors of a2 – 2ab + b2 are (a+b) and (a+b).

Lets factorize a2 – 2ab + b2 by splitting middle term.

a2 – 2ab + b2 = a2 – ab – ab + b2 [∵, -ab – ab = - 2ab & (-ab)(-ab) = a2b2]


⇒ a2 – 2ab + b2 = a(a – b) – b(a – b)


⇒ a2 – 2ab + b2 = (a – b)(a – b) = (a – b)2


So, the factors of a2 – 2ab + b2 are (a – b) and (a – b).


Hence, the statement is false.


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