Question: User: (1) (3x + 5)(2x + 7) = 6x² + □x + 35
10
21
(2) (2x + 5)(3x + 2) =
(3) (3x + 5)(x - 6) =
(4) (2x + 5)(3x - 2) =
(5) (2x + 3y)(4x - 5y) =
(6) (3x + 5)(5x - 8) =
(7) (-x + 8)(3x + 2) =
1. **Problem:** Expand and simplify the expression $$(3x + 5)(2x + 7)$$ and find the missing coefficient in $$6x^2 + \square x + 35$$.
2. **Formula:** Use the distributive property (FOIL method) for binomials:
$$ (a + b)(c + d) = ac + ad + bc + bd $$
3. **Apply FOIL:**
$$ (3x + 5)(2x + 7) = 3x \cdot 2x + 3x \cdot 7 + 5 \cdot 2x + 5 \cdot 7 $$
$$ = 6x^2 + 21x + 10x + 35 $$
4. **Combine like terms:**
$$ 6x^2 + (21x + 10x) + 35 = 6x^2 + 31x + 35 $$
5. **Answer:** The missing coefficient is $$31$$.
**Final expression:**
$$ (3x + 5)(2x + 7) = 6x^2 + 31x + 35 $$