Question: User: $(x+7)(x+2)$
$(x+7)(x-2)$
$(x-7)(x+2)$
The three expressions are shown in the center, with the top one near the upper-center circle, the second one centered below it, and the third one slightly lower in the center.
position_hint: center
1. **Problem Statement:**
We are given three expressions to expand:
$$ (x+7)(x+2), \quad (x+7)(x-2), \quad (x-7)(x+2) $$
2. **Formula Used:**
To expand expressions of the form $(a+b)(c+d)$, use the distributive property (FOIL method):
$$ (a+b)(c+d) = ac + ad + bc + bd $$
3. **Expand each expression:**
- For $$ (x+7)(x+2) $$:
$$ x \cdot x + x \cdot 2 + 7 \cdot x + 7 \cdot 2 = x^2 + 2x + 7x + 14 $$
Combine like terms:
$$ x^2 + (2x + 7x) + 14 = x^2 + 9x + 14 $$
- For $$ (x+7)(x-2) $$:
$$ x \cdot x + x \cdot (-2) + 7 \cdot x + 7 \cdot (-2) = x^2 - 2x + 7x - 14 $$
Combine like terms:
$$ x^2 + (-2x + 7x) - 14 = x^2 + 5x - 14 $$
- For $$ (x-7)(x+2) $$:
$$ x \cdot x + x \cdot 2 + (-7) \cdot x + (-7) \cdot 2 = x^2 + 2x - 7x - 14 $$
Combine like terms:
$$ x^2 + (2x - 7x) - 14 = x^2 - 5x - 14 $$
4. **Final answers:**
$$ (x+7)(x+2) = x^2 + 9x + 14 $$
$$ (x+7)(x-2) = x^2 + 5x - 14 $$
$$ (x-7)(x+2) = x^2 - 5x - 14 $$