Answer::
[tex]25x^2-80[/tex]Explanation:
Given the product:
[tex]\left(5x−4\sqrt{5}\right)\left(5x+4\sqrt{5}\right)[/tex]First, expand the brackets:
[tex]\begin{gathered} =5x\left(5x+4\sqrt{5}\right)−4\sqrt{5}\left(5x+4\sqrt{5}\right) \\ =(5x)^2+20x\sqrt{5}-20x\sqrt{5}-(4\sqrt{5})^2 \\ =(5x)^2-(4\sqrt{5})^2 \end{gathered}[/tex]We then simplify:
[tex]\begin{gathered} =5^2x^2-4^2\sqrt{5}^2 \\ =25x^2-16(5) \\ =25x^2-80 \end{gathered}[/tex]The simplified form of the product is:
[tex]25x^2-80[/tex]