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

2 Answers
Apr 4, 2018

(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!

Apr 4, 2018

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.