Question

Okay hopefully the picture went but I need help foiling this please

Answer 1

`x^(2)` -
`z^(2)` - 2z
`√(5)` - 5

Explanation:

This is the equation that you started off with:

(x - z -
`√(5)`)(x + z +
`√(5)`)

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 +
`√(5)`) -z(x + z +
`√(5)`) -
`√(5)`(x + z +
`√(5)`)

= x^2 + xz + x
`√(5)` -xz -z^2 - z
`√(5)` - x
`√(5)` - z
`√(5)` - 5

= x^2 - z^2 - 2z
`√(5)` - 5

or
`x^(2) - z^(2) - 2z√(5) - 5`