Question

How do you simplify `(x+3)(x-3)+(x+7)(x-3)`?

Answer 1

`2x^2 +4x-30`

Explanation:

`(x+3)(x-3)+(x+7)(x-3)`

One method would be to multiply the brackets out and collect the like terms together.
This seems a long and tedious method - we will end up with 8 terms which need to be simplified.

We can also use a factoring method because there is a common bracket in each term.

`(x+3)color(red)((x-3))+(x+7)color(red)((x-3))`

`color(red)((x-3))(x+3 +x+7)`

=`color(red)((x-3))(2x+10)`

=`2x^2 +10x-6x-30`

`2x^2 +4x-30`