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To factor \( 100x^2 - 16 \) completely, follow these steps:

1. **Recognize the common factor:** Both terms, \( 100x^2 \) and \( 16 \), have a common factor of 4. So, first, factor out the 4:
   \[
   100x^2 - 16 = 4(25x^2 - 4)
   \]

2. **Factor the remaining quadratic expression \( 25x^2 - 4 \):**
   Notice that \( 25x^2 - 4 \) is a difference of squares. Use the difference of squares formula, \( a^2 - b^2 = (a - b)(a + b) \), where \( a = 5x \) and \( b = 2 \):
   \[
   25x^2 - 4 = (5x - 2)(5x + 2)
   \]

3. **Write the completely factored form:**
   Substitute this back into the expression with the 4 factored out:
   \[
   100x^2 - 16 = 4(5x - 2)(5x + 2)
   \]

Thus, the completely factored form is \( 4(5x - 2)(5x + 2) \), which corresponds to the third option.

Do you want more details or have any questions?

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Here are 5 related questions to practice:
1. How do you factor \( 36x^2 - 9 \)?
2. What is the factored form of \( 81x^2 - 49 \)?
3. How can you factor \( 144x^2 - 25 \)?
4. What is the completely factored form of \( 64x^2 - 1 \)?
5. How do you identify a difference of squares?

**Tip:** Always look for common factors first before applying any advanced factoring techniques!

What is the completely factored form of 100x^2 - 16?

Learn how to factor the expression 100x^2 - 16 completely by using the difference of squares technique. Step-by-step solution for factoring 4(5x - 2)(5x + 2). Suitable for students in Grades 8-10.

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