1. **Problem:** Expand and simplify $ (x + 3)(x + 5) + 4(x - 2) $. 2. **Formula and rules:** - Use distributive property: $ (a + b)(c + d) = ac + ad + bc + bd $. - Simplify by combining like terms. 3. **Step-by-step solution:** 1. Expand $ (x + 3)(x + 5) $: $$ x \times x + x \times 5 + 3 \times x + 3 \times 5 = x^2 + 5x + 3x + 15 $$ 2. Combine like terms: $$ x^2 + 8x + 15 $$ 3. Expand $ 4(x - 2) $: $$ 4 \times x - 4 \times 2 = 4x - 8 $$ 4. Add the two expressions: $$ (x^2 + 8x + 15) + (4x - 8) = x^2 + 8x + 15 + 4x - 8 $$ 5. Combine like terms: $$ x^2 + (8x + 4x) + (15 - 8) = x^2 + 12x + 7 $$ **Final answer:** $$ x^2 + 12x + 7 $$