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How to Multiply Polynomials of Different Degrees

A polynomial is a mathematical expression containing more than one term, such as (a + b^2 +c). They are classified by their "degrees," which is the value of the highest exponent present in the polynomial (in this case, 2). Performing arithmetic functions on two polynomials is a simple affair, but can become more complex if they are of different degrees.

Instructions

- 1
  Select a term in one of the polynomials, preferably from the polynomial containing fewer terms.
  
  For example, with the polynomials (3x^2 + 2y^2) and (2x^3 - xy^2 + 3), we'll choose the first term, 3x^2.
- 2
  Apply the distributive property by multiplying every term of the other polynomial by this chosen term.
  
  This lends a set of products in our example consisting of 6x^5 - 3x^3y^2 + 9x^2.
- 3
  Repeat this process for each term in the smaller polynomial.
  
  Applying the distributive property for the second term lends 4x^3y^2 - 2xy^4 + 6y^2)
- 4
  Add or subtract the sets of products from each other as the signs of your chosen polynomial dictates, combining like terms when possible.
  
  In our two sets of products, two of the terms have the common base of x^3y^2, so these are combined in the final sum:
  
  6x^5 - 2xy^4 + (4x^3y^2 - 3x^3y^2) + 9x^2 + 6y^2
  
  This simplifies to:
  
  6x^5 - 2xy^4 + x^3y^2 + 9x^2 + 6y^2

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