How to multiply two binomials?
Understand the Problem
The question is asking for the method to multiply two binomials, which typically involves using the distributive property or FOIL method. This will help in finding the resulting polynomial from the multiplication.
Answer
The product of the binomials $(a + b)(c + d)$ is $ac + ad + bc + bd$.
Answer for screen readers
The product of the binomials $(a + b)(c + d)$ is $ac + ad + bc + bd$.
Steps to Solve
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Identify the binomials Let's denote the two binomials as $(a + b)$ and $(c + d)$.
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Use the FOIL method Apply the FOIL (First, Outside, Inside, Last) method to multiply the two binomials:
- First: Multiply the first terms: $a \cdot c$
- Outside: Multiply the outer terms: $a \cdot d$
- Inside: Multiply the inner terms: $b \cdot c$
- Last: Multiply the last terms: $b \cdot d$
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Combine the results Combine all the products from the FOIL method: $$ ac + ad + bc + bd $$
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Write the final expression The resulting polynomial from the multiplication of the two binomials is: $$ ac + ad + bc + bd $$
The product of the binomials $(a + b)(c + d)$ is $ac + ad + bc + bd$.
More Information
The process demonstrated here is commonly known as the FOIL method, which is particularly useful for multiplying binomials. Understanding this technique allows for efficient calculation in algebraic expressions and is foundational for polynomial operations.
Tips
- Forgetting to apply all four steps of FOIL. It's important to remember to multiply both the first, outside, inside, and last terms.
- Not combining like terms after multiplication, which can lead to an incorrect answer if any terms are missed.
