Multiplying Polynomials

• 1
  Sample problem.
  
  Copy the problem onto your own sheet of paper. Copying the problem will force you to notice everything, and it will keep you from having to look back and forth from the book to your paper while trying to figure out the first step at the same time.
  
  
• 2
  Multiply first term.
  
  Multiply the first term in the first polynomial by all terms in the second polynomial.
  
  
• 3
  Multiply second term.
  
  Multiply the second term in the first polynomial by all terms in the second polynomial. Repeat this process for each term in the first polynomial.
  
  
• 4
  Add all products.
  
  Add together all the products.
  
  
• 5
  Simplify.
  
  Simplify all terms (see next section for an explanation). This is the product of the polynomials.
  
  

Simplifying Polynomials

• 1
  Sample problem.
  
  Identify all terms that have the same bases (the same variables or letters) and the same exponents on each variable. These terms with the same exponents on the same variables are called "like terms."
  
  
• 2
  Move like terms.
  
  Put the like terms next to each other.
  
  
• 3
  Add like terms.
  
  Add the like terms by adding the coefficients (the numbers on the left). The variables and the exponents remain unchanged when these terms are added.