Question

How do you multiply `(sqrtt-y) (sqrtt+y)`?

Answer 1

`(sqrt(t)-y)(sqrt(t)+y)= t-y^2`

Explanation:

In general we have a standard formula called the difference of squares:
`color(white)("XX")(a^2-b^2) = (a-b)(a+b)`

This can be written in reverse as
`color(white)("XX")(a-b)(a+b) = a^2-b^2`

Substituting
`color(white)("XX")sqrt(t) " for "a`
and
`color(white)("XX")y " for " b`

we have
`color(white)("XX")(sqrt(t)-y)(sqrt(t)+y)`

`color(white)("XXX")= (sqrt(t))^2-y^2`

`color(white)("XXX")=t-y^2`