1. Problem statement: The formula is $v = J(l^2 - \frac{R h}{5})$. 2. Expand by distributing $J$ across the parentheses. Applying distribution gives $v = J l^2 - \frac{J R h}{5}$. 3. Combine terms into a single fraction and factor common factors. Multiply numerator and denominator to obtain $v = \frac{5 J l^2 - J R h}{5}$. Factor out $J$ from the numerator to get $v = \frac{J(5 l^2 - R h)}{5}$. 4. Solve for $R$ (assume $J \ne 0$ and $h \ne 0$) step-by-step. Divide both sides by $J$ to get $\frac{v}{J} = l^2 - \frac{R h}{5}$. Isolate the $R h$ term: $\frac{R h}{5} = l^2 - \frac{v}{J}$. Multiply by 5: $R h = 5(l^2 - \frac{v}{J})$. Solve for $R$: $R = \frac{5(l^2 - v/J)}{h}$. 5. Final forms (equivalent expressions): Original: $v = J(l^2 - \frac{R h}{5})$. Expanded: $v = J l^2 - \frac{J R h}{5}$. Single fraction / factored: $v = \frac{J(5 l^2 - R h)}{5}$.