§ 5.2

Multiplication of Polynomials

Blitzer, Algebra for College Students, 6e – Slide #2 Section 5.2

Multiplying Polynomials

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Multiply

yxyx 724 36

. 36 724 yxyx

127436 yyxx Rearrange factors

Multiply coefficients andadd exponents

127418 yx

31118 yx Simplify

Blitzer, Algebra for College Students, 6e – Slide #3 Section 5.2

Multiplying Polynomials

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Multiply . 7536 253 xxx

7536 253 xxx

765636 32353 xxxxx Distribute

Multiply coefficients andadd exponents

358 423018 xxx

Blitzer, Algebra for College Students, 6e – Slide #4 Section 5.2

Multiplying Polynomials

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Multiply . 22 bababa

22 bababa

2222 bababbabaa Multiply the trinomial by each term of the binomial

Multiply coefficients andadd exponents

2222 bbabbabbaabaaa 322223 babbaabbaa

33 ba

Distribute

Simplify

Note this: We multiply each term of the binomial by each term of the trinomial. We get 6 products in all.

Blitzer, Algebra for College Students, 6e – Slide #5 Section 5.2

Multiplying Polynomials - FOIL

dbcxbdaxcxaxdcxbax

Using the FOIL Method to Multiply Binomials

first

outside

inside

last F O I L

Product of First terms

Product of Outside terms

Product of Inside terms

Product of Last terms

Blitzer, Algebra for College Students, 6e – Slide #6 Section 5.2

Multiplying Polynomials - FOIL

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Multiply . 1534 xx

1534 xx 13531454 xxxx

Combine like terms

Multiply315420 2 xxx

31920 2 xx

F O I Lfirst

outside

inside

last

Blitzer, Algebra for College Students, 6e – Slide #7 Section 5.2

Multiplying Polynomials – Special Formulas

The Square of a Binomial Sum

22 BABABA

The Square of a Binomial Difference

222 2 BABABA

222 2 BABABA

The Product of the Sum and Difference of Two Terms

Blitzer, Algebra for College Students, 6e – Slide #8 Section 5.2

Multiplying Polynomials – Special Formulas

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Multiply .4 2yx

24 yx

222 2 BABABA

Use the special-product formula shown.

+ + = Product

+ +

2

Term

First

Terms theof

Product22

Term

Last

24x yx422y 22 816 yxyx

Blitzer, Algebra for College Students, 6e – Slide #9 Section 5.2

Multiplying Polynomials – Special Formulas

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Multiply . 43 2yx

243 yx

222 2 BABABA

Use the special-product formula shown.

- + = Product

- +

2

Term

First

Terms theof

Product22

Term

Last

23x yx 432 24y22 16249 yxyx

Blitzer, Algebra for College Students, 6e – Slide #10 Section 5.2

Multiplying Polynomials – Special Formulas

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Multiply . 4343 22 yxyyxy

222 4 3 yxy

22 BABABA

Use the special-product formula shown.

First Term Squared

Second Term Squared

Product- =

= 242 169 yyx

Blitzer, Algebra for College Students, 6e – Slide #11 Section 5.2

Multiplying Polynomials – Special Formulas

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

Multiply . 33 yxyx

92 22 yyxx

2A

We can group the terms so that the formula for the square of a binomial can be applied.

2B(A + B) (A - B) = - 22 333 yxyxyx

92 22 yxyx

Blitzer, Algebra for College Students, 6e – Slide #12 Section 5.2

Multiplying Polynomial Functions

EXAMPLEEXAMPLE

SOLUTIONSOLUTION

following. theofeach Find .10 and 4Let xxgxxf

4062 xx

(a) (fg)(x) = f (x) g(x)

404102 xxx

(a) (fg)(x)(b) (fg)(-1)(c) (fg)(0)

= (x - 4)(x + 10)F O I L

. 4062 xxxfgThus,

Blitzer, Algebra for College Students, 6e – Slide #13 Section 5.2

Multiplying Polynomial Functions

45401611 2 fg

CONTINUECONTINUEDD

(b) We use the product function to find (fg)(-1) – that is, the value of the function fg at -1. Replace x with -1.

40400600 2 fg

(c) We use the product function to find (fg)(0) – that is, the value of the function fg at 0. Replace x with 0.

5.2 Assignmentp.327 (2-8 even, 14-32 even, 40-50 even, 56, 58, 70, 72, 95, 96)