Question

What are the Special Products of Polynomials?

Answer 1

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`