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)x2−y2=(x+y)(x−y)

    (x + y)^2 = x^2 + y^2 + 2ab(x+y)2=x2+y2+2ab

    (x - y)^2 = x^2 + y^2 - 2ab(x−y)2=x2+y2−2ab

    Note: (x - y)^2 != x^2 - y^2(x−y)2≠x2−y2

    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)a2−b2=(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) x2−1=(x−1)(x+1)
    x^2 - 4 = (x-2)(x+2) x2−4=(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) x4−16=(x2)2−42=(x2−4)(x2+4)=(x−2)(x+2)(x2+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(x+y)2=x2+2xy+y2
    and
    (x−y)^2=x-2xy+y^2(x−y)2=x−2xy+y2
    and
    (x+y)(x−y)=x^2−y^2(x+y)(x−y)=x2−y2

    Two less well-known ones are
    x^3+y^3=(x+y)(x^2−xy+y^2)x3+y3=(x+y)(x2−xy+y2)
    and
    x^3−y^3=(x−y)(x^2+xy−y^2)x3−y3=(x−y)(x2+xy−y2)
    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