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

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

Answer :

To factor the expression [tex]\(16x^2 - 169y^2\)[/tex], you can recognize that it represents a difference of squares. The difference of squares formula states:

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

In this expression, we need to identify [tex]\(a^2\)[/tex] and [tex]\(b^2\)[/tex]:

1. Notice that [tex]\(16x^2\)[/tex] is a perfect square. We can write it as [tex]\((4x)^2\)[/tex].
2. Similarly, [tex]\(169y^2\)[/tex] is also a perfect square and can be written as [tex]\((13y)^2\)[/tex].

Now, applying the difference of squares formula:

Let [tex]\(a = 4x\)[/tex] and [tex]\(b = 13y\)[/tex].

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

So, the factored form of the expression [tex]\(16x^2 - 169y^2\)[/tex] is:

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

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