Multiply. Assume that all variables represent positive real numbers. \( (\sqrt{k}-t)(\sqrt{k}+t) \) \( (\sqrt{k}-t)(\sqrt{k}+t)=\square \) (Simplify your answer.)

To simplify \( (\sqrt{k}-t)(\sqrt{k}+t) \), we can use the difference of squares formula, which states that \( (a-b)(a+b) = a^2 - b^2 \). Here, \( a = \sqrt{k} \) and \( b = t \). Thus, we have: \[ (\sqrt{k}-t)(\sqrt{k}+t) = (\sqrt{k})^2 - t^2 = k - t^2 \] The simplified answer is \( k - t^2 \). Now, let’s delve into why this is useful in the real world: this form of expression often appears in algebra and calculus, especially when simplifying equations in physics or finance where variables represent quantities like distance (k) and time (t). Understanding how to simplify expressions quickly can save you time during problem-solving, showcasing the beauty of algebra! Furthermore, remember that a common mistake when applying the difference of squares is overlooking a sign change or misidentifying the variables. Always double-check if you applied the formula correctly by confirming that you consistently handled the positive and negative signs!