Multiplication of Polynomials by Binomials

Key Questions

  • What is FOIL?

    Answer:

    It's a rule.

    Explanation:

    It's a rule commonly used in factoring, meaning to start by multiplying the two first variables first, then outer, then inner, then last.
    Ex:
    If the things being multiplied is (x+1) by (x-2), you would multiply "x" and "x" first.
    x*x=x^2x⋅x=x2
    x*-2=-2xx⋅−2=−2x
    1*x=x1⋅x=x
    1*-2=-21⋅−2=−2
    The final answer would be: x^2-x-2x2−x−2

    Ingrette W. · 1 · Mar 20 2018
  • How do you use the distributive property when you multiply polynomials?

    The distribution property says that a*(b+c)=a*b+a*ca⋅(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(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(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)(a+b)(c+d)⋅(e+f)

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

    =ace+acf+ade+adf+bce+bcf+bde+bdf=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, xx's x^2x2's, etc.
    (there are no like terms in this example)

    MeneerNask · 1 · Jan 3 2015

Questions

Polynomials and Factoring