The given expression is:

\[
81 - 100x^2
\]

This is a difference of squares, which has the general form:

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

We can rewrite \( 81 - 100x^2 \) as:

\[
81 - 100x^2 = (9)^2 - (10x)^2
\]

Now applying the difference of squares formula:

\[
(9)^2 - (10x)^2 = (9 - 10x)(9 + 10x)
\]

Thus, the factorization of \( 81 - 100x^2 \) is:

\[
(9 - 10x)(9 + 10x)
\]

Would you like more details or have any further questions?

Here are some related questions:
1. How do you factor more complex differences of squares?
2. Can you factor expressions that aren't perfect squares?
3. What happens if the expression was \(81 + 100x^2\)?
4. How does factoring help in solving quadratic equations?
5. Can you simplify other types of polynomials similarly?

**Tip:** Always look for common patterns like the difference of squares, which can make factoring much easier!

Learn how to factor the expression 81 - 100x^2 using the difference of squares method. This step-by-step solution covers key algebraic concepts such as recognizing perfect squares and applying the formula a^2 - b^2 = (a - b)(a + b). Suitable for students in Grades 8-10.

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