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(x+a)(x+b)=x2+(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(x+a)(x+a)=(x+a)2=x2+2ax+a2, or
      (x-a)(x-a)=(x-a)^2=x^2-2ax+a^2(x−a)(x−a)=(x−a)2=x2−2ax+a2
      Example : (x+1)^2=x^2+2x+1(x+1)2=x2+2x+1
      Or: 51^2=(50+1)^2=50^2+2*50+1=2601512=(50+1)2=502+2⋅50+1=2601

    2. the two numbers are equal, and opposite sign:
      (x+a)(x-a)=x^2-a^2(x+a)(x−a)=x2−a2
      Example : (x+1)(x-1)=x^2-1(x+1)(x−1)=x2−1
      Or: 51*49=(50+1)(50-1)=50^2-1=249951⋅49=(50+1)(50−1)=502−1=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(a+b)2=a2+2ab+b2

    Ex. (2a + 3b)^2 = 4a^2 + 12ab + 9b^2(2a+3b)2=4a2+12ab+9b2

    marfre · 1 · Jul 8 2018

Questions

Polynomials and Factoring