Answer:
[tex]x^{2}[/tex] - [tex]z^{2}[/tex] - 2z[tex]\sqrt{5}[/tex] - 5
Step-by-step explanation:
This is the equation that you started off with:
(x - z - [tex]\sqrt{5}[/tex])(x + z + [tex]\sqrt{5}[/tex])
You can't really use FOIL on this because that's used in multiplying binomials, and this is a trinomial, but you can still break it up and simplify it this way:
(a + b + c)*(d + e + f) = (a(d + e +f)) + (b(d + e + f)) + (c(d + e + f))
So, applying that idea to the actual equation:
x(x + z + [tex]\sqrt{5}[/tex]) -z(x + z + [tex]\sqrt{5}[/tex]) - [tex]\sqrt{5}[/tex](x + z + [tex]\sqrt{5}[/tex])
= x^2 + xz + x[tex]\sqrt{5}[/tex] -xz -z^2 - z[tex]\sqrt{5}[/tex] - x[tex]\sqrt{5}[/tex] - z[tex]\sqrt{5}[/tex] - 5
= x^2 - z^2 - 2z[tex]\sqrt{5}[/tex] - 5
or [tex]x^{2} - z^{2} - 2z\sqrt{5} - 5[/tex]
