I am referring to

this document on Backlund transformations.

In this paper, one has equations (50),

$$

begin{align*}

(w_1+w_0)_x&=2lambda_1+frac{1}{2}(w_1-w_0)^2\

(w_2+w_0)_x&=2lambda_2+frac{1}{2}(w_2-w_0)^2

end{align*},

$$

and equations (51),

$$

begin{align*}

(w_{12}+w_1)_x&=2lambda_1+frac{1}{2}(w_{12}-w_1)^2\

(w_{21}+w_2)_x&=2lambda_2+frac{1}{2}(w_{21}-w_2)^2

end{align*},

$$

Then it is said:

subtract the difference of eqns (50) from the difference of eqns (51) to give

$$

0=4(lambda_2-lambda_1)+frac{1}{2}((w_{12}-w_1)^2-(w_{21}-w_2)^2-(w_1-w_0)^2+(w_2-w_0)^2)

$$

I do not understand what is meant.

What do I have to subtract from what?

I am confused.