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Let's factorize the given expressions.

1. \( 16x^2 - 81 \)

This is a difference of squares, which can be factored using the formula \( a^2 - b^2 = (a + b)(a - b) \).

Here, \( a = 4x \) and \( b = 9 \), so:

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

2. \( (x + 6)(x - 6) - (x - 6) \)

First, factor out the common factor \( (x - 6) \):

\[ (x + 6)(x - 6) - (x - 6) = (x - 6)[(x + 6) - 1] = (x - 6)(x + 5) \]

The factorizations are:
1. \( 16x^2 - 81 = (4x + 9)(4x - 9) \)
2. \( (x + 6)(x - 6) - (x - 6) = (x - 6)(x + 5) \)

Do you want more details on any of these factorizations or have any questions?

Here are 5 questions you can ask next:
1. How do you factorize cubic polynomials?
2. Can you explain how to solve quadratic equations by factoring?
3. What are the methods for factoring trinomials?
4. How do you complete the square for a quadratic expression?
5. Can you show examples of factoring by grouping?

**Tip:** When factoring polynomials, always look for the greatest common factor (GCF) first before applying other factoring methods.

Learn how to factorize polynomials 16x^2 - 81 and (x + 6)(x - 6) - (x - 6) with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomial factorization using the difference of squares formula. Suitable for high school students.

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