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To solve the problem \((7 - x)(7 + 3x)\), we need to expand the expression using the distributive property (also known as the FOIL method for binomials):

### Step 1: Expand the expression
\[
(7 - x)(7 + 3x) = 7 \cdot 7 + 7 \cdot 3x - x \cdot 7 - x \cdot 3x
\]

### Step 2: Simplify each term
\[
= 49 + 21x - 7x - 3x^2
\]

### Step 3: Combine like terms
\[
= 49 + (21x - 7x) - 3x^2
\]
\[
= 49 + 14x - 3x^2
\]

### Final simplified expression:
\[
= -3x^2 + 14x + 49
\]

### Answer:
The correct answer is **(c) \(-3x^2 + 14x + 49\)**.

Would you like more details or have any questions? Here are some related questions you might explore:

1. How does the distributive property work in expanding binomials?
2. What are common mistakes when expanding and simplifying expressions?
3. How do you identify like terms when simplifying algebraic expressions?
4. How does the FOIL method specifically help with binomial multiplication?
5. Can you apply these steps to a more complex expression, such as \((x - 4)(2x + 5)\)?

**Tip:** Always carefully combine like terms to ensure correct simplification when expanding expressions.

¿Cuál es el resultado de (7 - x)(7 + 3x)?

Learn how to simplify the expression (7 - x)(7 + 3x) using the distributive property. This step-by-step guide covers binomial multiplication and combining like terms. Ideal for students in Grades 8-10.

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