Multiplication of Monomials by Polynomials

Key Questions

  • What is Multiplication of Monomials by Polynomials?

    It works the same as with numbers. For numbers, you know that #a(b+c)# equals #ab+ac#.
    For the same reason, if you have a monomial and you want to multiplicate it by a polynomial (which is a sum of monomials with some coefficients!), you follow the same rule.

    For example, if your monomial is #3x^2#, and your polynomial is #3+2x-5x^2+8x^3#, the product is
    #3x^2(3+2x-5x^2+8x^3)#
    you will calculate is as
    #3x^2\cdot 3+3x^2\cdot2x-3x^2\cdot5x^2+3x^2\cdot8x^3#, which is
    #9x^2 + 6x^3 - 15x^4 + 24x^5#

    KillerBunny · 1 · Feb 1 2015
  • How do you multiply monomials by monomials?

    Answer:

    #=> a_1x^(p_1) * a_2x^(p_2)=a_1a_2x^(p_1+p_2)#

    Explanation:

    A monomial is of the form:

    #=> ax^p#

    where #a# is a constant coefficient and #p# is a constant power.

    In the case of multiplying two monomials together:

    #=>Ax^P equiv a_1x^(p_1) * a_2x^(p_2)#

    The coefficients will multiply, so:

    #=> A =a_1 * a_2#

    The powers will sum, so:

    #=> P =p_1 + p_2#

    Hence:

    #=> Ax^P equiv a_1x^(p_1) * a_2x^(p_2)=a_1a_2x^(p_1+p_2)#

    For example:
    #=>3x^2*2x#

    #=> (3*2)x^(2+1)#

    #=> 6x^3#

    NJ · 1 · Mar 27 2018
  • How do you multiply monomials by polynomials?

    Just distribute the monomial to each of the polynomial's terms

    For example:

    #(3m)(m^2 -2m + 1)#

    #=> (3m)(m^2) - (3m)(2m) + (3m)(1)#
    #=> 3m^3 - 6m^2 + 3m#

    seph · 1 · Oct 25 2014

Questions

Polynomials and Factoring