Factor. \( (c+t)^{2}-36 \) \( (c+t)^{2}-36=\square \) \( ( \) Factor completely.)

To factor the expression \( (c+t)^{2}-36 \), you can recognize that this is a difference of squares. This means you can rewrite it as \( (c+t)^{2} - 6^{2} \). According to the difference of squares formula \( a^{2} - b^{2} = (a-b)(a+b) \), we can apply it here. So, we have: \[ (c+t-6)(c+t+6) \] This gives the fully factored form of the original expression. Going a step further, you might notice that the expression you factored can represent real-world situations, like modeling the area of a square plot and how its dimensions might change (expand or contract) relative to a fixed size difference (in this case, 6). Whether planning a garden or a building, factoring helps clarify how dimensions influence total area! Also, when factoring, a common mistake is overlooking the difference of squares. Always remember to check if there are two squares being subtracted! If you miss this, you might attempt to factor through grouping or other methods that aren't applicable, leading to frustration. So, keep an eye out for those perfect squares!