How to Factor Using the Distributive Property

The distributive property is one of the most popular and easiest ways to multiply two values together. Using the distributive property, values of one polynomial are multiplied by either a single value or another polynomial. The distributive property helps to make sure each value is multiplied with all the other factors, and prevents errors. Multiplying several functions together can be confusing, and using the distributive property can help keep track of which factors have already been used.

Instructions

Multiplying one factor with a polynomial

1. Multiply the first number of the polynomial by the number outside the parentheses. For instance, if you have 3 (3x + 7y + 3z) you would multiply 3x by three, giving you 9x.

2. Multiply the second number of the polynomial by the number outside the parentheses. In the example 3 (3x + 7y + 3z) you would multiply 7y by three, giving you 21y.

3. Multiply the third number of the polynomial by the number outside the parentheses. In the example 3 (3x + 7y + 3z) you would multiple 3z by three, giving you 9z.

4. Record each value, and add them together. In our example the solution would be 9x + 21y + 9z.

Multiplying two polynomials

1. Multiply the first number of the first polynomial with the first number of the second polynomial. In the example (2x + 3y)(5x + 5y) you would multiply 2x times 5x to get 10x^2.

2. Multiply the first number of the first polynomial with the second number of the second polynomial. In the above example (2x + 3y)(5x + 5y) you would multiply 2x times 5y to get 2x5y, or 10xy. If there are more than two factors in the second polynomial, continue multiplying the value from the first polynomial with (i.e., distributing them to) each of the other factors in second polynomial.

3. Multiply the second number of the first polynomial with the first number of the second polynomial. In the example (2x + 3y)(5x + 5y), you would multiply 3y times 5x to get 15xy.

4. Multiply the second number of the first polynomial with the second number of the second polynomial. In the example (2x + 3y)(5x + 5y) you would multiply 3y times 5y to get 15y^2. If there are more than two factors in the second polynomial, continue multiplying the value from the first polynomial with (i.e., distributing them to) each of the other factors in second polynomial.

5. Add the numbers together. For the above example you will add the following: 10x^2 + 10xy + 15xy + 15y^2 which equals 10x^2 + 25xy + 15y^2.