# What are the Special Products of Polynomials?

Jan 5, 2015

The general form for multiplying two binomials is:
$\left(x + a\right) \left(x + b\right) = {x}^{2} + \left(a + b\right) x + a b$

Special products:

1. the two numbers are equal, so it's a square:
$\left(x + a\right) \left(x + a\right) = {\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$, or
$\left(x - a\right) \left(x - a\right) = {\left(x - a\right)}^{2} = {x}^{2} - 2 a x + {a}^{2}$
Example : ${\left(x + 1\right)}^{2} = {x}^{2} + 2 x + 1$
Or: ${51}^{2} = {\left(50 + 1\right)}^{2} = {50}^{2} + 2 \cdot 50 + 1 = 2601$

2. the two numbers are equal, and opposite sign:
$\left(x + a\right) \left(x - a\right) = {x}^{2} - {a}^{2}$
Example : $\left(x + 1\right) \left(x - 1\right) = {x}^{2} - 1$
Or: $51 \cdot 49 = \left(50 + 1\right) \left(50 - 1\right) = {50}^{2} - 1 = 2499$