Factor the polynomial completely.

81 x squared minus 1681x2−16

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Part 1

Select the correct choice below and fill in any answer boxes within your choice.

A.81 x squared minus 16 equals enter your response here

81 x squared minus 1681x2−16equals=enter your response here

We are asked to factor the polynomial \( 81x^2 - 16 \). Let's follow these steps to solve the problem.

### Step 1: Recognize it as a difference of squares.
The given polynomial is in the form \( a^2 - b^2 \), where:
- \( a^2 = (9x)^2 \)
- \( b^2 = 4^2 \)

So, we can rewrite the expression as:
\[
81x^2 - 16 = (9x)^2 - 4^2
\]

### Step 2: Apply the difference of squares formula.
The difference of squares formula is:
\[
a^2 - b^2 = (a - b)(a + b)
\]

Substitute \( a = 9x \) and \( b = 4 \):
\[
81x^2 - 16 = (9x - 4)(9x + 4)
\]

Thus, the factored form is:
\[
81x^2 - 16 = (9x - 4)(9x + 4)
\]

### Final Answer:
\[
81x^2 - 16 = (9x - 4)(9x + 4)
\]

Would you like further explanation on this process?

### Follow-up Questions:
1. How do you factor more complex polynomials?
2. What is the difference of squares rule, and when can it be applied?
3. How do you determine if a polynomial is factorable?
4. What other types of polynomial factorization exist?
5. Can you apply the difference of squares to cubic or quartic expressions?

### Tip:
Always check for common factors before applying any factoring techniques.

Factor the polynomial completely: 81x^2 - 16.

Learn how to factor the polynomial 81x^2 - 16 completely by applying the difference of squares formula. This step-by-step guide covers essential algebraic concepts for high school students in Grades 9-11.

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