Multiplying the Polynomials

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Sharp Tutor Mon, Jan 17, 2022 06:45 PM UTC

OBJECTIVES:
1. Multiply terms. 2. Multiply any two polynomials. 3. Multiply binomials. 4. Find the product of the sum and difference of two terms. 5. Find the square of a binomial. 6. Multiply polynomial functions.

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 6.4 - 1

2. Chapter 6
Exponents, Polynomials, and
Polynomial Functions
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 6.4 - 2

3. 6.4
Multiplying Polynomials
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 6.4 - 3

4. 6.4 Multiplying Polynomials
Objectives
1. Multiply terms.
2. Multiply any two polynomials.
3. Multiply binomials.
4. Find the product of the sum and difference
of two terms.
5. Find the square of a binomial.
6. Multiply polynomial functions.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 4

5. 6.4 Multiplying Polynomials
Multiplying Monomials
We multiply polynomials by using the distributive,
commutative, and associative properties along with the rules of
Multiply the numerical factors, then multiply
the variable factors.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 5

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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 6

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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 7

8. 6.4 Multiplying Polynomials
Multiplying the Product of Two Binomials by a Monomial
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 8

9. 6.4 Multiplying Polynomials
Multiplying Polynomials Vertically
Find the product.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 9

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
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 10

11. 6.4 Multiplying Polynomials
Using the FOIL Method
First terms Last terms
Inner terms
Outer terms
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 11

12. 6.4 Multiplying Polynomials
Product of the Sum and Difference of Two Terms
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 12

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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 17

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.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.4 - 19

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