What is the factored form of a^2 - 121?
Check the final answer first, then review the worked steps.
Problem
What is the factored form of a^2 - 121?
Answer
\((a - 11)(a + 11)\)
Step-by-step solution
- Identify the form of the expression: The given expression is $a^2 - 121$. This is a binomial expression. We need to determine if it fits any special factoring patterns.
- Recognize the difference of squares pattern: The expression $a^2 - 121$ can be rewritten as $a^2 - 11^2$. This is in the form of a difference of squares, which is $x^2 - y^2$.
- Apply the difference of squares formula: The difference of squares formula states that $x^2 - y^2 = (x - y)(x + y)$. In this case, $x = a$ and $y = 11$.
- Substitute values into the formula: Substituting $a$ for $x$ and $11$ for $y$ into the formula, we get $(a - 11)(a + 11)$.
- Verify the factorization: To verify, we can expand the factored form: $(a - 11)(a + 11) = a(a + 11) - 11(a + 11) = a^2 + 11a - 11a - 121 = a^2 - 121$. This matches the original expression.