What are the Special Products of Polynomials?

1 Answer
Jan 5, 2015

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#