Question

How do you simplify `(y ^ { 3} - 2y ^ { 2} - 3y + 4) - ( 2y ^ { 3} - y ^ { 2} + y - 3)`?

Answer 1

`-y^3-y^2-4y+7`

Explanation:

So we need to collect all of the like terms, ie. all `y^3`, `y^2` etc. Since there are two brackets we must expand the brackets, since the second bracket:

`(-1)(2y^3 - y^2 +y - 3)`

So we need to multiply all of the terms inside the brackets by -1, so all of the negative terms become positive and positive terms become negative.

`(-1)(2y^3 - y^2 +y - 3)`
`-2y^3 + y^2 - y +3`

The first bracket is simply multiplied by 1 so the expanded bracket is:

`y^3 -2y^2 - 3y +4`

Now add the other bracket:

`y^3 -2y^2 - 3y +4-2y^3 + y^2 - y +3`

All of the terms are now outside the bracket meaning we can add like terms:

`-y^3-y^2-4y+7`