Q. 1 G3.5( 13 Votes )

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Answer :

If (a + b)2 = a2 + 2ab + b2


Then (x + y)2 – 4xy


= x2 + 2xy + y2-4xy


= x2 + y2-2xy


In given expression


1st and last terms are perfect square


x2 = x × x


y2 = y × y


And the middle expression is in form of 2ab


2xy = 2 × x × y


x × x - 2 × y × x + y × y


Gives (a-b)2 = a2-2ab + b2


In x2 – 2xy + y2


a = x and b = y;


x2 – 2xy + y2 = (x-y)2


Hence the factors of (x + y)2 – 4xy are (x-y)and (x-y)


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