Special Products of Polynomials

Key Questions

  • What are the Special Products of Polynomials?

    The general form for multiplying two binomials is:
    #(x+a)(x+b)=x^2+(a+b)x+ab#

    Special products:

    1. the two numbers are equal, so it's a square:
      #(x+a)(x+a)=(x+a)^2=x^2+2ax+a^2#, or
      #(x-a)(x-a)=(x-a)^2=x^2-2ax+a^2#
      Example : #(x+1)^2=x^2+2x+1#
      Or: #51^2=(50+1)^2=50^2+2*50+1=2601#

    2. the two numbers are equal, and opposite sign:
      #(x+a)(x-a)=x^2-a^2#
      Example : #(x+1)(x-1)=x^2-1#
      Or: #51*49=(50+1)(50-1)=50^2-1=2499#

    MeneerNask · 1 · Jan 5 2015
  • What is a perfect square binomial and how do you find the product?

    Answer:

    A trinomial that when factored gives you the square of a binomial

    Explanation:

    Given: What is a perfect square binomial?

    A perfect square binomial is a trinomial that when factored gives you the square of a binomial.

    Ex. #(a+b)^2 = a^2 + 2ab + b^2#

    Ex. #(2a + 3b)^2 = 4a^2 + 12ab + 9b^2#

    marfre · 1 · Jul 8 2018

Questions

Polynomials and Factoring