Multiply: [ (4+sqrt(2))(4-sqrt(2)) ] 4-sqrt(2) 14 16-sqrt(2) 18

To multiply \((4+\sqrt{2})(4-\sqrt{2})\), we can use the difference of squares formula, which states that \((a+b)(a-b) = a^2 - b^2\).<br /><br />Here, \(a = 4\) and \(b = \sqrt{2}\). Applying the formula:<br /><br />\[<br />(4+\sqrt{2})(4-\sqrt{2}) = 4^2 - (\sqrt{2})^2<br />\]<br /><br />Now, calculate each term:<br /><br />\[<br />4^2 = 16<br />\]<br />\[<br />(\sqrt{2})^2 = 2<br />\]<br /><br />So,<br /><br />\[<br />(4+\sqrt{2})(4-\sqrt{2}) = 16 - 2 = 14<br />\]<br /><br />Therefore, the correct answer is:<br /><br />\[<br />14<br />\]