Answer :
We are given the expression
[tex]$$
x^2 - 169.
$$[/tex]
Notice that [tex]$169$[/tex] is a perfect square since [tex]$169 = 13^2$[/tex]. Thus, the expression can be written as
[tex]$$
x^2 - 13^2.
$$[/tex]
This is a difference of squares, which factors according to the formula
[tex]$$
a^2 - b^2 = (a - b)(a + b).
$$[/tex]
Here, [tex]$a = x$[/tex] and [tex]$b = 13$[/tex]. Applying the formula, we obtain
[tex]$$
x^2 - 13^2 = (x - 13)(x + 13).
$$[/tex]
Hence, the factorization of [tex]$x^2 - 169$[/tex] is
[tex]$$
(x - 13)(x + 13).
$$[/tex]
[tex]$$
x^2 - 169.
$$[/tex]
Notice that [tex]$169$[/tex] is a perfect square since [tex]$169 = 13^2$[/tex]. Thus, the expression can be written as
[tex]$$
x^2 - 13^2.
$$[/tex]
This is a difference of squares, which factors according to the formula
[tex]$$
a^2 - b^2 = (a - b)(a + b).
$$[/tex]
Here, [tex]$a = x$[/tex] and [tex]$b = 13$[/tex]. Applying the formula, we obtain
[tex]$$
x^2 - 13^2 = (x - 13)(x + 13).
$$[/tex]
Hence, the factorization of [tex]$x^2 - 169$[/tex] is
[tex]$$
(x - 13)(x + 13).
$$[/tex]
