Question

How much less is x² − 2xy + 3y² than 2x² − 3y² + xy?

Answer 1

$$\begin{gathered} \begin{array}{l}\text{We have:}\\ \text{(}2x^2-3y^2+xy)-(x^2-2xy+3y^2)\end{array} \\ =2x^2-3y^2+xy-x^2+2xy-3y^2) \\ \begin{array}{l}=2x^2-x^2-3y^2-3y^2+xy+2xy\\ =x^2-6y^2+3xy\end{array} \\ \therefore x^2-2xy+3y^2\mathrm{is}\mathrm{less}\mathrm{than}2x^2-3y^2+xby{x}^2-6y^2+3xy. \end{gathered}$$