Question

How do you combine like terms in `(7y ^ { 2} + 4y + 3) + ( - 2y ^ { 2} + 3y - 4) - ( 9y ^ { 2} + 5y - 6)`?

Answer 1

`-4y^2 + 2y + 5`

Here's how I did it:

Explanation:

`(7y^2+4y+3)+(-2y^2+3y-4)-(9y^2+5y-6)`

First, let's distribute the negative sign in `-(9y^2+5y-6)`:
`-9y^2-5y+6`

So now...
`7y^2+4y+3-2y^2+3y-4-9y^2-5y+6`

Let's colorize the like terms for easier read:
`color(red)(7y^2) + color(magenta)(4y) + color(blue)(3) quadcolor(red)(-quad2y^2) + color(magenta)(3y) quadcolor(blue)(-quad4) quadcolor(red)(-quad9y^2) quadcolor(magenta)(-quad5y) + color(blue)(6)`

Now let's combine the like terms:
`color(red)(7y^2-2y^2-9y^2) = -4y^2`

`color(magenta)(4y + 3y - 5y) = 2y`

`color(blue)(3 - 4 + 6) = 5`

And when we combine them together we get:
`-4y^2 + 2y + 5`

Hope this helps!