Resolve into factors: (a+b)^{2}-2(a^{2}-b^{2} | vedclass

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(C) Given expression: $(a+b)^{2}-2(a^{2}-b^{2})+(a-b)^{2}$We know that $(a^{2}-b^{2}) = (a+b)(a-b)$.Substituting this into the expression:$(a+b)^{2}-2

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$4 b^{2}$

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(C) Given expression: $(a+b)^{2}-2(a^{2}-b^{2})+(a-b)^{2}$We know that $(a^{2}-b^{2}) = (a+b)(a-b)$.Substituting this into the expression:$(a+b)^{2}-2(a+b)(a-b)+(a-b)^{2}$This is in the form of $x^{2}-2xy+y^{2}$,where $x = (a+b)$ and $y = (a-b)$.Using the identity $(x-y)^{2} = x^{2}-2xy+y^{2}$,we get:$\{(a+b)-(a-b)\}^{2}$$= (a+b-a+b)^{2}$$= (2b)^{2}$$= 4b^{2}$

Resolve into factors: $(a+b)^{2}-2(a^{2}-b^{2})+(a-b)^{2}$

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