1. **Problem:** Simplify the expression $$(5x - 2)(x + 4) - (2x + 1)(5x - 3) + 5x^2.$$ 2. **Formula and rules:** Use distributive property (FOIL) to expand each product, then combine like terms carefully. 3. **Step 1: Expand each product** $$(5x - 2)(x + 4) = 5x \cdot x + 5x \cdot 4 - 2 \cdot x - 2 \cdot 4 = 5x^2 + 20x - 2x - 8 = 5x^2 + 18x - 8.$$ $$(2x + 1)(5x - 3) = 2x \cdot 5x + 2x \cdot (-3) + 1 \cdot 5x + 1 \cdot (-3) = 10x^2 - 6x + 5x - 3 = 10x^2 - x - 3.$$ 4. **Step 2: Substitute expansions back into the expression** $$5x^2 + 18x - 8 - (10x^2 - x - 3) + 5x^2.$$ 5. **Step 3: Distribute the minus sign to the second group** $$5x^2 + 18x - 8 - 10x^2 + x + 3 + 5x^2.$$ 6. **Step 4: Combine like terms** - Combine $x^2$ terms: $$5x^2 - 10x^2 + 5x^2 = \cancel{5x^2} - \cancel{10x^2} + \cancel{5x^2} = 0.$$ - Combine $x$ terms: $$18x + x = 19x.$$ - Combine constants: $$-8 + 3 = -5.$$ 7. **Final simplified expression:** $$19x - 5.$$ **Answer:** (d) $19x - 5$