Question 60 (b)

What should be subtracted from $- 7 m n + 2 m^{2} + 3 n^{2}$ to get $m^{2} + 2 m n + n^{2} ?$

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Solution

In order to get solution, we will subtract $m^{2} + 2 m n + n^{2}$ from $- 7 m n + 2 m^{2} + 3 n^{2} .$
Required expression is
$- 7 m n + 2 m^{2} + 3 n^{2} - (m^{2} + 2 m n + n^{2}) = - 7 m n + 2 m^{2} + 3 n^{2} - m^{2} - 2 m n - n^{2}$
On combining the like terms,
$= - 7 m n - 2 m n + 2 m^{2} - m^{2} + 3 n^{2} - n^{2} = - 9 m n + m^{2} + 2 n^{2}$
So, if we subtract $m^{2} + 2 n^{2} - 9 m n$ from $- 7 m n + 2 m^{2} + 3 n^{2}$ , then we get $m^{2} + 2 m n + n^{2} .$

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