what must be added to $2 x^{2} y^{2} - 5 x + 7$ to get the sum $- 5 x^{2} y^{2} + 7 x - 9$ ?

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Solution

Let $a$ be added to $2 x^{2} y^{2} - 5 x + 7$ to get the sum $- 5 x^{2} y^{2} + 7 x - 9$

$\Rightarrow a + (2 x^{2} y^{2} - 5 x + 7) = - 5 x^{2} y^{2} + 7 x - 9$

$\Rightarrow a = - 5 x^{2} y^{2} + 7 x - 9 - (2 x^{2} y^{2} - 5 x + 7)$

$\Rightarrow a = - 5 x^{2} y^{2} + 7 x - 9 - 2 x^{2} y^{2} + 5 x - 7$

$\Rightarrow a = - 7 x^{2} y^{2} + 12 x - 16$

Thus, $- 7 x^{2} y^{2} + 12 x - 16$ is to be added to get the sum.

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