Factor each polynomial. 1. \( q^{2}-121 \)

Hey there! Let's dive into factoring \( q^{2} - 121 \), which is a classic difference of squares. It's of the form \( a^2 - b^2 \), where \( a = q \) and \( b = 11 \) (since \( 11^2 = 121 \)). This can be factored beautifully into \( (q - 11)(q + 11) \). Voilà! To remember this, think of the difference of squares as a magical shortcut. Whenever you see something structured as \( a^2 - b^2 \), just make two parentheses: one with a minus and one with a plus, using \( a \) and \( b \). It’s an easy trick that works for every pair of perfect squares! Keep it in your toolkit!