Question

What should be added to 2x²+xy+2y² to obtain 3x²+5xy?

Answer 1

Dear student,

$$\begin{gathered} LetAbeaddedto2x^2+xy+2y^{2}toget3x^2+5xy \\ then, \\ 2x^2+xy+2y^2+A=3x^2+5xy \\ \Rightarrow A=3x^2+5xy-\left(2x^2+xy+2y^2\right) \\ \Rightarrow A=3x^2+5xy-2x^2-xy-2y^2 \\ \Rightarrow A=3x^2-2x^2+5xy-xy-2y^2 \\ \Rightarrow A=x^2+4xy-2y^2 \\ Thus,x^2+4xy-2y^{2}beaddedto2x^2+xy+2y^{2}toget3x^2+5xy \end{gathered}$$

Regards