Multiplying Polynomials

The following are rules regarding the multiplying of variable expressions.

• Rule 1: To multiply monomials with the same base, keep the base and add the powers:
  

  
  

• Rule 2: To find the power of a base, keep the base and multiply the powers.
  

  
  

• Rule 3: To find a power of a product, raise each factor in the product to the power.
  

  
  

Example 1: Simplify each of the following multiplication problems and state which rule above was applied.

To multiply monomials together, follow this procedure.

1. Multiply the numerical coefficients together.

2. Multiply the variables together.

3. Multiply the results together.

Example 2: Simplify each of the following.

To multiply polynomials together, multiply each term in one polynomial by each term in the other polynomial. Then simplify if possible.

Example 3: Multiply each of the following.

The following shows how each equation is multiplied both horizontally and vertically.

Equation (a) done horizontally.

Equation (a) done vertically.

Equation (b) done horizontally.

Equation (b) done vertically.

Equation (c) done horizontally.

= x³ + y³

Equation (c) done vertically.

Cite this article