Question
\( \equiv 1 \quad \equiv 2 \quad \equiv 4: 50 \) Factor. \( \quad=2 \quad=6 \) \( w^{2}-25 \)
Ask by Coles Ray. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( w^2 - 25 \) factors to \( (w - 5)(w + 5) \).
Solution
1. Recognize that the expression is a difference of squares:
\[
w^2 - 25 = w^2 - 5^2
\]
2. Recall the general formula for factoring a difference of squares:
\[
a^2 - b^2 = (a-b)(a+b)
\]
3. In this case, let \( a = w \) and \( b = 5 \). Substitute into the formula:
\[
w^2 - 5^2 = (w-5)(w+5)
\]
4. Therefore, the factorization of \( w^2 - 25 \) is:
\[
(w-5)(w+5)
\]
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Simplify this solution Mind Expander
Let's dive into factoring \( w^{2} - 25 \). This expression is a classic example of the difference of squares, which can be factored using the formula \( a^{2} - b^{2} = (a - b)(a + b) \). In this case, we identify \( a = w \) and \( b = 5 \). Thus, we can rewrite the expression as \( (w - 5)(w + 5) \). Now, when you encounter expressions like this, remember that recognizing patterns can make the process smoother and quicker! Also, a common mistake is trying to factor incorrectly such as finding common factors where there are none. Just look for those perfect squares!
