Multiply a Trinomial and a Binomial
Learning Outcome
- Multiply and divide polynomials
Example
Find the product.Answer: Distribute the trinomial to each term in the binomial. Use the distributive property to distribute the monomials to each term in the trinomials. Multiply. Group like terms. Combine like terms.
Example
Multiply.Answer: Set up the problem in a vertical form, and begin by multiplying by . Place the products underneath, as shown. Now multiply by . Notice that ; since this term is like , place it directly beneath it. Finally, multiply by . Notice that is placed underneath . Now add like terms. The answer is .
Example
Find the product.Answer:
Another way to keep track of all the terms involved in the above product is to use a table, as shown below. Write one polynomial across the top and the other down the side. For each box in the table, multiply the term for that row by the term for that column. Then add all of the terms together, combine like terms, and simplify. Notice how we kept the sign on each term; for example, we are subtracting from , so we place in the table.
Example
Multiply.Answer: Distribute and to each term in the trinomial.
Multiply. Notice that the subtracted and the subtracted have a positive product that is added.
Combine like terms.