Multiplication of Polynomials and Polynomial Multiplication Formulas

To multiply polynomials:

1. Expand the expression using the distributive property.
2. Combine like terms if there are any.

Multiplication of Polynomials Using the Area of a Rectangle

Multiplication Formula (1)

1. Square of a Sum or Difference
   
   
2. Product of a Sum and a Difference
   

Notes:

Multiplication Formula (2)

1. Product of Two Linear Expressions with Coefficient of Equal to
   
2. Product of Two Linear Expressions with Coefficient of Not Equal to
   

Applications of Multiplication Formulas

1. Expanding Expressions with Common Parts
   Assign a common part to a variable, expand, and substitute back:
   
2. Using Multiplication Formulas for Numerical Calculations
1. Calculating Squares of Numbers
   Use or :
   
   
   
   
2. Calculating the Product of Two Numbers
   Use or :
   
   
   

Calculations Involving Square Roots Using Multiplication Formulas

1. Using Multiplication Formulas for Square Root Calculations
   Treat square roots as variables and use multiplication formulas:


2. Rationalizing Denominators Using Multiplication Formulas
   When the denominator contains two terms involving square roots, use the formula to rationalize:
   Provided and ,
   

Variations of Multiplication Formulas