Q. 2 J4.0( 9 Votes )

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Answer :

In the given expression p2 – 2pq + q2


1st and last terms are perfect square


p2 = p × p


q2 = q × q


And the middle expression is in form of 2ab


2pq = 2 × p × q


p × p - 2 × p × q + q × q


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


In p2 – 2pq + q2


a = p and b = q;


p2 – 2pq + q2 = (p-q)2


Now the given expression is (p-q)2– r2


Both terms are perfect square


(p-q)2 = (p-q) × (p-q)


r2 = r × r


(p-q)2– r2 Seems to be in identity a2-b2 = (a + b)(a-b)


Where a = (p-q) and b = r;


(p-q)2– r2 = (p-q-r) (p-q + r)


Hence the factors of (p2 – 2pq + q2) – r2 are (p-q-r) and (p-q + r)


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