Expert Answers

An illustration of the letter 'A' in a speech bubbles

You should open the brackets such that:

`u^3 + v^3 + 2 + 3uv(u+v) - 4(u+v) = 0`

You need to group the terms such that:

`(u^3 + v^3 + 3uv(u+v))- 4(u+v) = 0`

Notice that the first group represents th expansion of the following:

`(u+v)^3 = u^3 + v^3...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

You should open the brackets such that:

`u^3 + v^3 + 2 + 3uv(u+v) - 4(u+v) = 0`

You need to group the terms such that:

`(u^3 + v^3 + 3uv(u+v))- 4(u+v) = 0`

Notice that the first group represents th expansion of the following:

`(u+v)^3 = u^3 + v^3 + 3uv(u+v)`

Hence, you should substitute `(u+v)^3`  for `u^3 + v^3 + 3uv(u+v)`  such that:

`(u+v)^3 - 4(u+v) = 0`

You need to factor out `u+v`  such that:

`(u+v)((u+v)^2 - 4) = 0`

Setting each factor equal to zero yields:

`u + v = 0 => u = -v`

`(u+v)^2 - 4 = 0 => u+v = +-2`

Since `u=-v` , then the second equation contradicts the first, hence, the solutions to the given equation are `u,v in R` .

Approved by eNotes Editorial Team