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------------------------------------------------ Factor [tex]16x^2 - 169y^2[/tex].

[tex]16x^2 - 169y^2 = [/tex]

To factor the expression [tex]\(16x^2 - 169y^2\)[/tex], we will use the difference of squares method. The difference of squares formula is given by:

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

First, let's identify [tex]\(a^2\)[/tex] and [tex]\(b^2\)[/tex] in the expression [tex]\(16x^2 - 169y^2\)[/tex]:

1. [tex]\(16x^2\)[/tex] can be written as [tex]\((4x)^2\)[/tex].
2. [tex]\(169y^2\)[/tex] can be written as [tex]\((13y)^2\)[/tex].

Now, inside the expression [tex]\(16x^2 - 169y^2\)[/tex], we have two perfect squares:

- [tex]\(a = 4x\)[/tex]
- [tex]\(b = 13y\)[/tex]

Now apply the difference of squares formula:

[tex]\[ 16x^2 - 169y^2 = (4x)^2 - (13y)^2 = (4x - 13y)(4x + 13y) \][/tex]

So, the factored form of the expression is:

[tex]\[(4x - 13y)(4x + 13y)\][/tex]

That's the step-by-step solution for factoring the expression [tex]\(16x^2 - 169y^2\)[/tex].