The expression \((w + 7)^2\) is a perfect square trinomial. To expand it, use the formula:

\[
(a + b)^2 = a^2 + 2ab + b^2
\]

Here, \(a = w\) and \(b = 7\). Applying the formula:

\[
(w + 7)^2 = w^2 + 2(w)(7) + 7^2
\]

Simplify:

\[
(w + 7)^2 = w^2 + 14w + 49
\]

### Final Answer:
\[
(w + 7)^2 = w^2 + 14w + 49
\]

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### 5 Related Questions:
1. How do you expand \((w - 7)^2\)?
2. What is the general formula for \((a + b)^2\) and \((a - b)^2\)?
3. How does \((w + 7)^2\) differ from \((w + 7)(w - 7)\)?
4. Can you show the process of factoring back from \(w^2 + 14w + 49\) to \((w + 7)^2\)?
5. How would \((2w + 7)^2\) expand?

### Tip:
Always remember to double-check your coefficients when using the distributive property or expansion formulas to avoid mistakes!

Learn how to expand and simplify the expression (w + 7)² using the formula for perfect square trinomials. This detailed guide breaks down the steps to derive w² + 14w + 49, covering key algebraic concepts. Suitable for students in Grades 7-9.

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