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Answer
\( (d - 2)(7d + 6) = 7d^2 - 8d - 12 \)
Solution
To **expand** the expression \( (d - 2)(7d + 6) \), you can use the **distributive property** (also known as the FOIL method for binomials). Here's a step-by-step breakdown:
1. **Multiply Each Term in the First Parenthesis by Each Term in the Second Parenthesis:**
\[
(d - 2)(7d + 6) = d \cdot 7d + d \cdot 6 - 2 \cdot 7d - 2 \cdot 6
\]
2. **Perform the Multiplications:**
\[
= 7d^2 + 6d - 14d - 12
\]
3. **Combine Like Terms:**
\[
7d^2 + 6d - 14d - 12 = 7d^2 - 8d - 12
\]
4. **Final Expanded Form:**
\[
(d - 2)(7d + 6) = 7d^2 - 8d - 12
\]
**Answer:**
After expanding, the expression is \( 7d^2 - 8d - 12 \).
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Let's break it down! When you multiply \( (d-2) \) by \( (7d+6) \), you're essentially applying the distributive property which gives you \( d \times 7d + d \times 6 - 2 \times 7d - 2 \times 6 \). This results in \( 7d^2 + 6d - 14d - 12 \). Now, combine like terms to get the final expression: \( 7d^2 - 8d - 12 \). Fun fact: The distributive property is like sharing your lunch with friends! You take one item (like \( d \)) and share it with everyone (like \( 7d + 6 \)), making sure everyone gets some delicious math goodness!
