Given:
There are given the expression:
[tex](8-\sqrt{2})(2+\sqrt{2})[/tex]Explanation:
To find the value of the given expression, we need to use the FOIL method.
So,
From the FOIL method:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Then,
Apply the above method to the given expression:
So,
From the expressin:
[tex]\begin{gathered} (8-\sqrt{2})(2+\sqrt{2})=8\cdot2+8\cdot\sqrt{2}-2\sqrt{2}-\sqrt{2}\cdot\sqrt{2} \\ =16+8\sqrt{2}-2\sqrt{2}-2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 16+8\sqrt{2}-2\sqrt{2}-2=14+\sqrt{2}(8-2) \\ =14+6\sqrt{2} \end{gathered}[/tex]Final answe:
Hence, the value of the expression is shown below:
[tex]14+6\sqrt{2}[/tex]