1. **State the problem:** Simplify the expression $(7x^2 - 3y) - (3x^2 + 5y)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to the second group: $$7x^2 - 3y - 3x^2 - 5y$$ 3. **Group like terms:** Combine terms with $x^2$ and terms with $y$: $$ (7x^2 - 3x^2) + (-3y - 5y) $$ 4. **Simplify each group:** $$ 7x^2 - 3x^2 = 4x^2 $$ $$ -3y - 5y = -8y $$ 5. **Write the final simplified expression:** $$4x^2 - 8y$$