Factor completely.

81, minus, 16, x, squared

81−16*x*2

To factor the expression \(81 - 16x^2\) completely, we recognize it as a difference of squares. The formula for factoring a difference of squares is:

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

### Step 1: Identify \(a\) and \(b\)
In this case:
- \(a^2 = 81\) so \(a = 9\) (since \(9^2 = 81\))
- \(b^2 = 16x^2\) so \(b = 4x\) (since \((4x)^2 = 16x^2\))

### Step 2: Apply the Difference of Squares Formula
Now we can apply the formula:

\[
81 - 16x^2 = (9 - 4x)(9 + 4x)
\]

### Final Answer
The completely factored form of the expression is:

\[
(9 - 4x)(9 + 4x)
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you factor \(49 - 25y^2\)?
2. Can you apply the difference of squares to \(100 - z^2\)?
3. What happens if you have a sum of squares, like \(9 + 16x^2\)?
4. How do you recognize and factor other polynomial identities?
5. How would you factor \(25 - 36x^2\)?

**Tip**: Always look for the difference of squares in expressions, as it allows for straightforward factoring into binomials.

Explore how to completely factor the expression 81 - 16x^2 using the difference of squares formula. This guide covers essential algebra concepts suitable for students in Grades 7-9.

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