Multiplying Polynomials (Box and Distributive Methods)

When multiplying polynomials, remember the rules of exponents

1. when multiplying same bases, add exponents

2. when dividing same bases, subtract exponents

3. when raising a power to a power, multiply exponents

4. any number to the zero power is 1

1. Create a box divided into columns and rows equal to the number of terms in each polynomial

2. Write one polynomial across the top of the box, with each term corresponding to a cell. Put the sign of the term in the cell with the polynomial.

3. Write the other polynomial down the side of the box, with each term corresponding to a cell.

4. Put the sign of the term next to the term, not above

5. Multiply the upper polynomial by the first term of the side polynomial and write it in the cell underneath the term

6. Multiply the upper polynomial by the second term of the side polynomial and write it in the cell underneath the term

7. Continue until you have multiplied the top polynomial by every term in the side polynomial

8. Simplifying by adding like terms.

Notice the like terms follow a diagonal line

1. Called the rainbow method because of the lines of distribution

2. Multiply everything in the second polynomial by the first term in the first polynomial (along with the sign)

3. Multiply everything in the second polynomial by the second term (along with the sign)

4. Continue the process until there are no more terms in the first polynomial to multiply by

5. Simplify by combining like terms.