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10.3 – Multiplying Binomials
Key Terms
 Constant Polynomials – Polynomials of degree 0.
 A constant polynomial has no variable.
 Distributive Property – The rule that if a, b, and c are numbers or expressions, then .
 FOIL – A method of multiplying binomials. FOIL stands for First, Outer, Inner, Last: the order in which you would multiply a binomial’s terms.
 Linear Polynomial – A polynomial of degree 1.
 A linear polynomial has a variable term and may also have a constant term.
Review
Remember… 
 The area of a rectangle is the number of square units it covers.
 Degree
 Don’t confuse the degree of a polynomial with the number of terms in the polynomial.
 The degree of a polynomial is its greatest exponent.
 x is a polynomial of degree 1 because . It’s because there is only ONE x, not because x has only 1 term.
 ALWAYS write your answers in descending order (greatest to smallest degree).
 Tiles
 Notice that the tile tool assumes that all terms are separated by plus signs (+).
 Why? Because a polynomial is a sum of terms.
 Factors
 A factor is a number or expression that is multiplied.
 A product is the answer to a multiplication problem.
 The commutative property of multiplication applies to polynomials and their factors.
 The order of the factors does not change the product.
This can also be written as:

Notes
The Distributive Property 
 Using tiles is helpful for multiplying constant polynomials and linear polynomials, but if you need to multiply higherdegree polynomials, you need to use the distributive property.
 You can find the product of ANY two binomials using the distributive property .
 In the distributive property, a, b, and c can be numbers, variables, entire variable expressions, or polynomials (which ARE variable expressions).
 Another example

FOIL – First, Outer, Inner, Last 
 Multiplying Binomials Using FOIL

Examples
Important!
Practice (Apex Study 10.3)
 Try practice problems on Pgs 7, 16, 24
 Mandatory: write and answer problems on Pgs 8, 17, 23
 3 Quizzes
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