2. Exponents, Polynomials, and Polynomial Functions
Chapter 6
Exponents, Polynomials, and
Polynomial Functions

3. Multiplying Polynomials
6.4
Multiplying Polynomials

4. 6.4 Multiplying Polynomials
Objectives
Multiply terms.
Multiply any two polynomials.
Multiply binomials.
Find the product of the sum and difference of two terms.
Find the square of a binomial.
Multiply polynomial functions.
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5. 6.4 Multiplying Polynomials
Multiplying Monomials
We multiply polynomials by using the distributive, commutative, and associative properties along with the rules of exponents.
Multiply the numerical factors, then multiply the variable factors.
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6. 6.4 Multiplying Polynomials
Multiplying a Polynomial by a Monomial
To multiply a polynomial with more than one term by a monomial, use the distributive property to remove parentheses and simplify.
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7. 6.4 Multiplying Polynomials
Multiplying a Binomial by a Binomial
To multiply two binomials, multiply each term of one binomial by each term of the other binomial and combine like terms.
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8. 6.4 Multiplying Polynomials
Multiplying the Product of Two Binomials by a Monomial
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9. 6.4 Multiplying Polynomials
Multiplying Polynomials Vertically
Find the product.
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10. 6.4 Multiplying Polynomials
Using the FOIL Method
We can use a shortcut method, called the FOIL method, to multiply binomials. FOIL is an acronym for First terms, Outer terms, Inner terms, and Last terms. To use the FOIL method to multiply 2a – 4 by 3a + 5, we
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11. 6.4 Multiplying Polynomials
Using the FOIL Method
First terms
Last terms
Inner terms
Outer terms
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12. 6.4 Multiplying Polynomials
Product of the Sum and Difference of Two Terms
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13. 6.4 Multiplying Polynomials
Finding the Square of a Binomial
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14. 6.4 Multiplying Polynomials
Finding the Square of a Binomial
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15. 6.4 Multiplying Polynomials
Finding the Square of a Binomial
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16. 6.4 Multiplying Polynomials
Multiplying More Complicated Polynomials
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17. 6.4 Multiplying Polynomials
Multiplying Polynomial Functions
In Section 6.3, we saw how functions could be added and subtracted. Functions can also be multiplied.
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18. 6.4 Multiplying Polynomials
Multiplying Polynomial Functions
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19. 6.4 Multiplying Polynomials
Multiplying Polynomial Functions
Another way of arriving at the same answer is to find
and then multiply the results to obtain –16.
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