Question

How do you multiply polynomials `(a + b - c)(a + b + c)`?

Answer 1

`(a+b-c)(a+b+c) = a^2+2ab+b^2-c^2`

Explanation:

Note that:

`(A-B)(A+B) = A^2-B^2`

So putting `A=(a+b)` and `B=c` we find:

`(a+b-c)(a+b+c) = ((a+b)-c)((a+b)+c)`

`color(white)((a+b-c)(a+b+c)) = (a+b)^2-c^2`

`color(white)((a+b-c)(a+b+c)) = a^2+2ab+b^2-c^2`