Question

Subtract by horizontal method : ${\mathrm{x}}^2-{\mathrm{y}}^2$ from ${\mathrm{x}}^2+{\mathrm{y}}^2$

Answer 1

To subtract an algebraic expression form another , add the negative of the first expression to the second .

In other words , change the sign of each of the terms of the first expression and proceed as you would in the case of addition.

$$\begin{gathered} =({\mathrm{x}}^2+{\mathrm{y}}^2)-({\mathrm{x}}^2-{\mathrm{y}}^2) \\ =({\mathrm{x}}^2+{\mathrm{y}}^2)+(-{\mathrm{x}}^2+{\mathrm{y}}^2) \\ ={\mathrm{x}}^2+{\mathrm{y}}^2-{\mathrm{x}}^2+{\mathrm{y}}^2 \\ ={\mathrm{x}}^2-{\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{y}}^2 \\ =0+2{\mathrm{y}}^2 \\ =2{\mathrm{y}}^2 \end{gathered}$$

Hence , $2{\mathrm{y}}^2$ is the difference between the given algebraic expressions