Question

What is the possible answer for `(sqrt10-5)(sqrt10+2)`? How to simplify the answer? Thank you for the help.

Answer 1

`-3sqrt10`

Explanation:

Think of this as basically `(a-b)(a+c)` and how you would expand it which would be `a(a+c)-b(a+c)=a^2+ac-ab-bc`

So `(sqrt10-5)(sqrt10+2) = sqrt10 (sqrt10+2)-5(sqrt10+2) = 10+2sqrt10-5sqrt10-10 = -3sqrt10`

Answer 2

`color(magenta)(-3 sqrt 10`

Explanation:

`color(white)(aaaaaaaaaaaaa)` `sqrt10-5`
`color(white)(aaaaaaaaaaa)` `xx underline(sqrt10+2)`
`color(white)(aaaaaaaaaaaaa)` `10-5sqrt10`
`color(white)(aaaaaaaaaaaaaaaa)` `+2 sqrt 10-10`
`color(white)(aaaaaaaaaaaaa)` `overline(10-3 sqrt 10-10)`

`color(white)(aaaaaaaaaaaaa)` `color(magenta)(-3 sqrt 10`