Multiplying polynomials example | Polynomial and rational functions | Algebra II | Khan Academy

TL;DR

Learn how to multiply a binomial by a trinomial by using the distributive property.

Transcript

Multiply (5a - 2)(4a^2 + 3a - 1) So here we are multiplying a binomial by a trinomial So the FOIL tool will not work here It would only work if you were multiplying a binomial by another binomial So here we really have to rely on the distributive property. What we can do is we can distribute this entire trinomial onto the binomial. We we can multip... Read More

Key Insights

• ✖️ Multiplying a binomial by a trinomial requires using the distributive property.
• 😑 Like terms can be combined to simplify the expression.
• ✖️ The FOIL method is not applicable when multiplying a binomial by a trinomial.

Questions & Answers

Q: Can I use the FOIL method to multiply a binomial by a trinomial?

No, the FOIL method only works when multiplying a binomial by another binomial. For a binomial and trinomial, the distributive property must be used.

Q: What do I do when multiplying a binomial by the first term of a trinomial?

Multiply each term of the binomial by the first term of the trinomial and combine like terms.

Q: How do I handle the second part of the multiplication, where the binomial is multiplied by the second term of the trinomial?

Multiply each term of the binomial by the second term of the trinomial and combine like terms.

Q: Can I use a different method to achieve the same result?

Yes, you can also approach the multiplication by multiplying the binomial by each term of the trinomial separately and then combining like terms. This method is analogous to how we multiply numbers.

Summary & Key Takeaways

• Multiplying a binomial by a trinomial requires using the distributive property.

• Break down the multiplication into two parts: multiplying the binomial by the first term of the trinomial, and then multiplying the binomial by the second term of the trinomial.

• Combine like terms to simplify the expression.