Question

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

Answer 1

`color(blue)(2x^2+4x-30)`

Explanation:

We can use the FOIL Method,
(First, Outer, Inner, and Last)

like this,

`(a+b)(c+d) = ac + ad + bc + cd`

Solving the problem,

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

we can simplify the 1st term, `(x+3)(x-3)`

`(x+3)(x-3) = x^2 -3x+3x-9`

`x^2 -3x+3x-9`, combine all like terms, to simplify, if there is any, like `-3x` and `+3x`, we can combine this.

Since `a + (-a) = 0` (Additive Inverse Property), we can cancel the like terms giving,

`= x^2 - 9`

now apply FOIL method, to the 2nd term.

`(x+7)(x-3) = x^2-3x+7x-21`

simplify, by combining like terms,

`= x^2+4x-21`

Plug it all,

`x^2 - 9 + x^2+4x-21`

combine like terms to simplify again, we must simplify the answer as long as possible.

`= 2x^2+4x-30`