1. **Problem statement:** Solve the system of equations: $$\begin{cases} s + c = m \\ s - c = 2 \end{cases}$$ Find the value of $s \times c$. 2. **Formula and rules:** To solve the system, add the two equations to eliminate $c$: $$ (s + c) + (s - c) = m + 2 $$ Simplify: $$ s + \cancel{c} + s - \cancel{c} = m + 2 $$ $$ 2s = m + 2 $$ Divide both sides by 2: $$ s = \frac{m + 2}{2} $$ 3. Substitute $s$ back into the first equation to find $c$: $$ s + c = m $$ $$ c = m - s = m - \frac{m + 2}{2} $$ Simplify: $$ c = \frac{2m}{2} - \frac{m + 2}{2} = \frac{2m - (m + 2)}{2} = \frac{2m - m - 2}{2} = \frac{m - 2}{2} $$ 4. Calculate $s \times c$: $$ s \times c = \left(\frac{m + 2}{2}\right) \times \left(\frac{m - 2}{2}\right) = \frac{(m + 2)(m - 2)}{4} $$ 5. Use the difference of squares formula: $$ (m + 2)(m - 2) = m^2 - 4 $$ So, $$ s \times c = \frac{m^2 - 4}{4} $$ **Final answer:** $$ s \times c = \frac{m^2 - 4}{4} $$