Question

How do you use the distributive property when you multiply polynomials?

Answer 1

The distribution property says that `a*(b+c)=a*b+a*c`

With more polynomials it gets a bit harder. I'll do it the long way:

`(a+b)*(c+d)=(a+b)*c+(a+b)*d`

We have distributed the second binomial, and we now distribute the first binomial (twice):

`(a+b)*c+(a+b)*d=a*c+b*c+a*d+b*d`

With larger polynomials the 'book-keeping' may become a bit tedious, and most trained people take shortcuts.

If you have more than two polynomials, best method is to do them step by step, two at a time:

`(a+b)(c+d)*(e+f)`

`=(ac+ad+bc+bd)(e+f)` (see above)

`=ace+acf+ade+adf+bce+bcf+bde+bdf`

Last check: 2-term times 2-term = 4 terms
4-terms times 2-term = 8-terms.
In practical examples, you will be able to add like terms (like the numbers, `x`'s `x^2`'s, etc.
(there are no like terms in this example)