Question

How do you find the product of `(x-3)^2`?

Answer 1

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

From here we can just FOIL; first, outer, inner, last. Multiply the first term in the first bracket (x), by the FIRST term in the second bracket (x), giving us `x^2`. Then, we multiply the outermost term on the left side by the OUTERmost on the right side, giving us `-3 * x`, equal to `-3x`. We then multiply the INNERmost terms together, which are again -3 and `x`, giving us `-3x` again. Finally we multiply the LAST term in the first bracket by the last term of the second, giving us `-3 * -3`, or 9. Then, we simply write these out, in order:

`x^2-3x-3x+9`

Collect like terms:

`x^2-6x+9`

And you're done!

Answer 2

`x^3-6x+9`

Explanation:

1. Let's say `A=x-3` (this is to help you understand).
   So then we would have `A^2`, which gets you `AxxA`.

2. Now let's apply that back into the original problem.
   `(x-3)^2=(x-3)xx(x-3)=(x-3)(x-3)`

3. We can use the Distributive Property to make this more easily readable:
   `\color(red)(x(x-3))+\color(green)((-3)(x-3))`
   Simplify by re-applying Distributive Property:
   `\color(red)(x(x)+x(-3))+\color(green)((-3)(x)+(-3)(-3))`

4. And multiply...
   `x^2+(-3x)+(-3x)+9=x^3-6x+9`

`\color(tomato)(\text(For the third step:))` This is really just me explaining FOIL in a different way.