$3 x + 23 x^{2} + 6 y^{2} + 2 x + y^{2} +____________= 5 x + 7 y^{2} .$

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Solution

We have, $3 x + 23 x^{2} + 6 y^{2} + 2 x + y^{2} +____________= 5 x + 7 y^{2} .$
Let the unknown quantity be $a$ .
$\begin{array}{rcl} 3 x + 23 x^{2} + 6 y^{2} + 2 x + y^{2} + a & = & 5 x + 7 y^{2} \\ 3 x + 2 x - 5 x + 23 x^{2} + 6 y^{2} + y^{2} - 7 y^{2} & = & - a \\ - a & = & 5 x - 5 x + 7 y^{2} - 7 y^{2} + 23 x^{2} \\ - a & = & 23 x^{2} \\ a & = & - 23 x^{2} \end{array}$
Hence, the answer is $- 23 x^{2}$ .

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