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m2-mn+n2 what should be added to make it a perfect square

how to find this?

Hi!

The given expression is m2 – mn + n2.
We know that, m2 – 2mn + n2 = (m – n)2
(m2 – 2mn + n2 ) – (m2 – mn + n2 ) = –mn
Thus, –mn should be added to m2 – mn + n2 in order to make it a perfect square.

Cheers!

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View Full Answer

Remember the identity: (a-b)2 = a2 - 2ab + b2 .

In the quesiton m2 - mn + n2 . We need to make the middle term as 2mn, so we will add -mn to m2 - mn + n2  to make it a perfect square.

m2 - mn + n2-mn = m2 - 2mn + n2 = (m-n)2.

Hope this answers your quesiton

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