Question

How do you find the sum or difference of `(8y-4y^2)+(3y-9y^2)`?

Answer 1

`11y-13y^2`

Explanation:

When adding or subtracting you can not mix 'types' (variables)

`color(blue)("One method of several:")`

`8y-4y^2`
`ul(3y-9y^2) larr" add"`
`11y-13y^2`

`color(white)()`

`"+++++++++++++++++++++++++++++++++++"`
`"+++++++++++++ "color(blue)("Additional teaching")" +++++++++"`
`"+++++++++++++++++++++++++++++++++++"`

`color(brown)("When multiplying numbers if the signs are the same the answer is")` `color(brown)("positive. If the signs are different the answer is negative.")`

Suppose that instead of adding the two brackets we had a subtraction.

`(8y-4y^2)-(3y-9y^2)`

Think of:
`(8y-4y^2)` as `+1(8y-4y^2)`

Multiply everything inside the bracket by +1 giving:

`8y-4y^2`
..........................................................................

Think of:
`-(3y-9y^2)` as `-1(3y-9y^2)`

Multiply everything inside `(3y-9y^2)` by -1 giving:

`-3y+9y^2`
.......................................................................
Sometimes it is helpful to think of add as 'put with' and subtract as 'remove from'

`ul("Putting")" it all together ( put with "-> +") we have:"`

`color(white)(..)8y-4y^2`
`ul(-3y+9y^2) larr" add"`
`color(white)(..)5y+5y^2`