Lesson 2.6
Multiplying Polynomials
Multiplication is more powerful than addition — every term in the first polynomial must be distributed to every term in the second. FOIL is just a special case of this universal rule.
Introduction
You already know how to FOIL two binomials from Algebra 1. Now we extend this idea: every term in the first polynomial multiplies every term in the second.
Past Knowledge
You can FOIL: .
Today's Goal
Multiply any two polynomials, including binomial × trinomial.
Future Success
Multiplying is the foundation for polynomial division — you need it for the "Multiply" step in long division.
Key Concepts
1. The Universal Rule
Every term × Every term. Multiply each term in the first polynomial by each term in the second, then combine like terms.
A binomial × trinomial has 2 × 3 = 6 partial products
2. Exponent Rule
When multiplying like bases, add the exponents:
Example:
3. Special Products
Two patterns worth memorizing:
Perfect Square Trinomial
Difference of Squares
🚫 The #1 Mistake
≠
You are MISSING the middle term!
Worked Examples
Example 1: Monomial × Polynomial
BasicSimplify .
Distribute to Each Term
Final Answer
Example 2: Binomial × Trinomial
IntermediateExpand .
Distribute to Each Term
Distribute to Each Term
Combine Like Terms
Example 3: Special Product Trap
AdvancedExpand .
Rewrite as Multiplication
Apply the Formula (or FOIL)
Common Wrong Answer
≠ . The middle term is required.
Common Pitfalls
Missing the Middle Term
, NOT . Always FOIL or use the formula — never just "square each piece."
Forgetting to Add Exponents
, NOT . When multiplying, you add exponents. When raising a power to a power, you multiply.
Real-Life Applications
If a garden has dimensions by , the area is the product . Engineers, architects, and physicists multiply polynomial expressions constantly when computing areas, volumes, and forces.
Practice Quiz
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