To find the factored form of the expression [tex]\( a^2 - 121 \)[/tex], we can recognize that it fits the pattern of a difference of squares. The general form for factoring a difference of squares is:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
In this case, we can see that:
[tex]\[ a^2 - 121 \][/tex]
First, identify the square roots of the terms:
- [tex]\( a^2 \)[/tex] is [tex]\( (a)^2 \)[/tex]
- [tex]\( 121 \)[/tex] is [tex]\( (11)^2 \)[/tex]
This allows us to rewrite the expression as:
[tex]\[ a^2 - 11^2 \][/tex]
Now, using the difference of squares formula [tex]\( a^2 - b^2 = (a - b)(a + b) \)[/tex], we substitute [tex]\( a \)[/tex] for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] for [tex]\( 11 \)[/tex]:
[tex]\[ a^2 - 11^2 = (a - 11)(a + 11) \][/tex]
So, the factored form of [tex]\( a^2 - 121 \)[/tex] is:
[tex]\[ (a - 11)(a + 11) \][/tex]
Therefore, the correct answer is:
[tex]\[ (a - 11)(a + 11) \][/tex]
