Q. What should be added to $x^2+xy +y^2 to obtain 2x^2+3xy ?$ 

Dear Student,

$$\begin{gathered} 6. \left(a\right) \left(3x - y + 11\right) + \left(- y - 11\right) - \left(3x - y - 11\right) \\ = \cancel{3x} - y + \cancel{11} - \cancel{y} - \cancel{11} - \cancel{3x} + \cancel{y} + 11 \\ = - y + 11 \\ \left(b\right) \left\{\left(4 + 3x\right) + \left(5 - 4x + 2x^2\right)\right\} - \left\{\left(3x^2 - 5x\right) + \left(-x^2 + 2x + 5\right)\right\} \\ = \left(4 + 3x + 5 - 4x + 2x^2\right) - \left(3x^2 - 5x - x^2 + 2x + 5\right) \\ = \left(2x^2 - x + 9\right) - \left(2x^2 - 3x + 5\right) \\ = \cancel{2x^2} - x + 9 - \cancel{2x^2} + 3x - 5 \\ = 2x + 4 \end{gathered}$$

 

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