Question

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

Answer 1

Mathematica operation with algebraic expressions.

Let us consider that $m$ should be added to $x^2+xy+y^2$ to obtain$2x^2+3xy$.

$$\begin{gathered} \therefore m+(x^2+xy+y^2)=2x^2+3xy \\ \Rightarrow m=2x^2+3xy-(x^2+xy+y^2) \\ \Rightarrow m=2x^2+3xy-x^2-xy-y^2 \\ \Rightarrow m=2x^2-x^2+3xy-xy-y^2 \\ \Rightarrow m=x^2+2xy-y^2 \end{gathered}$$

Hence, the expression $x^2+2xy-y^2$should be added to $x^2+xy+y^2$ to obtain$2x^2+3xy$.