Question

How do you FOIL `(s^2+t)(s^2-t)`?

Answer 1

Given `color(red)((s^2+t))color(blue)((s^2-t))`

First terms: `color(red)(s^2) and color(blue)(s^2)`
Outside terms: `color(red)(s^2) and color(blue)((-t))`
Inside terms: `color(red)(t) and color(blue)(s^2)`
Last terms: `color(red)(t) and color(blue)(-t)`

The FOIL method is to
Sum

the product of the First terms (`s^2xxs^2 = s^4`)
the product of the Outside terms (`s^2xx(-t) = (-s^2t)`)
the product of the Inside terms (`t xx s^2 = s^2t`)
and
the product of the Last terms (`txx(-t) = (-t^2)`

For the given example this sum is `s^4-t^2`