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.