Question

what is the factored form of $a^2 - 121$?
$(a - 121)(a - 1)$
$(a - 11)(a + 11)$
$(a + 11)(a + 11)$
$(a - 121)(a + 1)$

Explanation:

Step1: Recognize difference of squares

The expression $a^2 - 121$ is a difference of squares, since $121 = 11^2$, so it fits $x^2 - y^2$.

Step2: Apply difference of squares formula

The difference of squares formula is $x^2 - y^2 = (x-y)(x+y)$. Substitute $x=a$, $y=11$:
$a^2 - 11^2 = (a-11)(a+11)$

Step3: Match with options

Compare the result to the given multiple-choice options.

Answer:

B. $(a - 11)(a + 11)$