Question

How do you multiply `(x - 1)(x + 1)(x - 3)(x + 3)`?

Answer 1

`(x-1)(x+1)(x-3)(x+3) = x^4-10x^2+9`

Explanation:

Note the difference of squares identity:

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

So we find:

`(x-1)(x+1) = x^2-1^2 = x^2-1`

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

Then if it helps, we can use FOIL to multiply out the resulting two binomials:

`(x^2-1)(x^2-9)`

`=overbrace((x^2 * x^2))^"First" + overbrace(((x^2) * (-9)))^"Outside" + overbrace(((-1) * (x^2)))^"Inside" + overbrace(((-1) * (-9)))^"Last"`

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

`=x^4-(9+1)x^2+9`

`=x^4-10x^2+9`