Answer :
[tex](\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = -22[/tex]
Solution:
Given that we have to multiply the given expression
Given is:
[tex](\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})[/tex]
We have to multiply the above expression
Apply the difference of two squares formula
[tex](a+b)(a-b) = a^2-b^2[/tex]
Similarly for,
[tex](\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8})[/tex]
We have,
[tex]a = \sqrt{10}\\\\b = 2\sqrt{8}[/tex]
Thus the equation becomes,
[tex](\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = (\sqrt{10})^2 - (2\sqrt{8})^2\\\\Simplify\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =(\sqrt{10} \times \sqrt{10}) - (2\sqrt{8} \times 2\sqrt{8})[/tex]
Use the below rule,
[tex]\sqrt{a} \times \sqrt{a} = a[/tex]
Therefore, the above equation becomes,
[tex](\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =10 - 4 \times 8\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) = 10 - 32\\\\(\sqrt{10} + 2\sqrt{8})(\sqrt{10} - 2\sqrt{8}) =-22[/tex]
Thus upon multiplying the given expression, solution is -22