Question: User: (5c-2d) (7c+5d
1. **State the problem:**
Multiply the two binomials $$(5c - 2d)(7c + 5d)$$.
2. **Formula used:**
Use the distributive property (FOIL method) for multiplying binomials:
$$(a + b)(x + y) = ax + ay + bx + by$$
3. **Apply the formula:**
$$(5c)(7c) + (5c)(5d) + (-2d)(7c) + (-2d)(5d)$$
4. **Calculate each term:**
$$35c^2 + 25cd - 14cd - 10d^2$$
5. **Combine like terms:**
$$35c^2 + (25cd - 14cd) - 10d^2 = 35c^2 + 11cd - 10d^2$$
6. **Final answer:**
$$(5c - 2d)(7c + 5d) = 35c^2 + 11cd - 10d^2$$