Question

multiply and simplify. (\\(\sqrt{6}+6\\))(\\(\sqrt{6}-6\\)) (\\(\sqrt{6}+6\\))(\\(\sqrt{6}-6\\)) = (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Apply difference - of - squares formula

Use the formula $(a + b)(a - b)=a^{2}-b^{2}$, where $a = \sqrt{6}$ and $b = 6$. So we have $(\sqrt{6}+6)(\sqrt{6}-6)=(\sqrt{6})^{2}-6^{2}$.

Step2: Calculate the squares

$(\sqrt{6})^{2}=6$ and $6^{2}=36$. Then $(\sqrt{6})^{2}-6^{2}=6 - 36$.

Step3: Subtract

$6-36=-30$.

Answer:

$-30$