Factor Polynomials Using Special Products

Key Questions

  • How do you identify special products when factoring?

    Answer:

    You identify special products by their values if its a perfect square or cubes..

    Explanation:

    For examples;

    Difference of two squares is: #x^2 - y^2 = (x + y) (x - y)#

    #(x + y)^2 = x^2 + y^2 + 2ab#

    #(x - y)^2 = x^2 + y^2 - 2ab#

    Note: #(x - y)^2 != x^2 - y^2#

    This Link might help!

    Jumbotron · 1 · Jul 21 2018
  • What is the difference of two squares method of factoring?

    There's a single formula which refers to "difference of squares":

    #a^2 - b^2 = (a-b)(a+b)#

    If we use FOIL we can prove that. Difference of squares method would refer to doing something like the following:

    #x^2 -1 = (x - 1)(x+1) #
    #x^2 - 4 = (x-2)(x+2) #

    Or even the double application here
    #x^4 - 16 = (x^2)^2 - 4^2 = (x^2 - 4)(x^2 + 4) = (x-2)(x+2)(x^2+4) #

    Jake M. · 1 · Mar 27 2018
  • How do you factor special products of polynomials?

    Look for numbers that are perfect squares or perfect cubes.
    There are many special products in factoring. Three of the most well-known are
    #(x+y)^2=x^2+2xy+y^2#
    and
    #(x−y)^2=x-2xy+y^2#
    and
    #(x+y)(x−y)=x^2−y^2#

    Two less well-known ones are
    #x^3+y^3=(x+y)(x^2−xy+y^2)#
    and
    #x^3−y^3=(x−y)(x^2+xy−y^2)#
    Note that in an actual problem, x and y can be any number or variable. Hope this helped!

    Sidharth · 1 · Jan 24 2015

Questions

Polynomials and Factoring