the equation 2s2=502*s*2=50 factors as 2(*s*−5)(*s*+5). how did they get this

The confusion here seems to be about how the factoring process works. Let's break down how the equation \(2s^2 = 50\) can be factored as \(2(s - 5)(s + 5)\).

### Step-by-Step Explanation

1. **Start with the equation:**

   \[
   2s^2 = 50
   \]

2. **Simplify by dividing both sides by 2:**

   \[
   s^2 = 25
   \]

3. **Recognize this as a difference of squares:**

   The expression \(s^2 - 25 = 0\) is a classic example of a difference of squares. It can be factored using the identity:

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

   Here, \(a = s\) and \(b = 5\), so:

   \[
   s^2 - 25 = (s - 5)(s + 5)
   \]

4. **Bring the factor of 2 back:**

   Since we divided by 2 earlier, we now multiply the factored expression by 2 to return to the original equation:

   \[
   2(s^2 - 25) = 2(s - 5)(s + 5)
   \]

5. **Check the factorization:**

   To verify, you can expand the factored form:

   \[
   2(s - 5)(s + 5) = 2(s^2 - 25) = 2s^2 - 50
   \]

   This is the original equation, confirming the factorization is correct.

So, the factorization \(2(s - 5)(s + 5)\) is derived from recognizing the difference of squares in \(s^2 - 25\) and then reintroducing the factor of 2.

Would you like more details or have any other questions?

Here are some related questions:

1. What is the difference of squares, and how is it factored?
2. How can you factor expressions that are not perfect squares?
3. What are some examples of factoring more complex quadratic equations?
4. How do you use the quadratic formula to solve any quadratic equation?
5. Can you factor quadratic equations with coefficients greater than 1?
6. How does completing the square help in solving quadratic equations?
7. What role does factoring play in solving quadratic inequalities?
8. How do you apply factoring in real-world problem-solving?

**Tip:** Identifying special factoring patterns, like the difference of squares, can make factoring quicker and easier.

Learn how to solve the equation 2s^2 = 50 by factoring. This detailed explanation covers the difference of squares method and demonstrates step-by-step how to factorize 2s^2 = 50 into 2(s - 5)(s + 5). Suitable for high school students.

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