00i ALG1 A CRM C08 TP 660282 - St. Johns County School …teachers.stjohns.k12.fl.us/santiago-alejandro-c/files/... · · 2016-12-17a. =-+ =-+ 8-4 Answers. a +) = + +-) =-+ +)(-)

Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

PDF Pass

Chapter 8 A11 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 8

24

Gle

ncoe

Alg

ebra

1

Spre

adsh

eet

Act

ivit

yM

ult

iply

ing

Po

lyn

om

ials

Exer

cise

sU

se t

he

spre

adsh

eet

to f

ind

th

e va

lue

of x

th

at a

llow

s th

e b

ox w

ith

th

e gr

eate

st

volu

me

for

each

pie

ce o

f ca

rdb

oard

. Sta

te t

he

volu

me

of t

he

box

.

1. 1

6 in

ches

lon

g an

d 10

in

ches

wid

e 2.

24

inch

es l

ong

and

18 i

nch

es w

ide

2

; 14

4 in

3 3

; 64

8 in

3

3. 2

8 in

ches

lon

g an

d 16

in

ches

wid

e

4. 3

6 in

ches

lon

g an

d 24

in

ches

wid

e

3;

660

in3

5;

1820

in3

5. 4

8 in

ches

lon

g an

d 48

in

ches

wid

e 6.

108

in

ches

lon

g an

d 44

in

ches

wid

e

8;

8192

in3

10;

21,

120

in3

7. S

tudy

th

e sp

read

shee

t yo

u c

reat

ed f

or E

xerc

ise

5. S

upp

ose

y is

th

e vo

lum

e of

th

e bo

x w

ith

a h

eigh

t of

x i

nch

es. I

f yo

u w

ere

to g

raph

th

e or

dere

d pa

irs

(x, y

) an

d co

nn

ect

them

w

ith

a s

moo

th c

urv

e, w

hat

wou

ld y

ou e

xpec

t th

e gr

aph

to

look

lik

e? U

se t

he

grap

hin

g to

ol i

n t

he

spre

adsh

eet

to v

erif

y yo

ur

con

ject

ure

. S

amp

le a

nsw

er: T

he

gra

ph

w

ou

ld r

ise

fro

m (

0, 0

) to

th

e p

oin

t w

her

e x g

ives

th

e g

reat

est

volu

me

and

th

en f

all b

ack

do

wn

to

war

d t

he

x-a

xis.

A

box

is

mad

e b

y cu

ttin

g a

squ

are

wit

h

sid

es x

in

ches

lon

g fr

om e

ach

cor

ner

of

ap

iece

of

card

boa

rd a

nd

fol

din

g u

p t

he

sid

es. I

f th

e p

iece

of

car

db

oard

is

15 i

nch

es l

ong

and

12

inch

es w

ide,

wh

at

inte

ger

valu

e of

x a

llow

s yo

u t

o m

ake

the

box

wit

h t

he

grea

test

vol

um

e? W

hat

is

the

volu

me?

Ste

p 1

T

he

fin

ish

ed b

ox w

ill

be x

in

ches

hig

h, 1

2 -

2x

inch

es

wid

e, a

nd

15 -

2x

inch

es l

ong.

Th

e vo

lum

e of

th

e bo

x is

x(1

2 -

2x)

(15

- 2

x) c

ubi

c in

ches

.

Ste

p 2

U

se C

olu

mn

A o

f th

e sp

read

shee

t fo

r th

e va

lue

of x

. E

nte

r th

e fo

rmu

las

for

the

wid

th, l

engt

h, a

nd

volu

me

in C

olu

mn

s B

, C, a

nd

D.

A1 3 4 5 6 72

BC

DW

idth

Leng

thV

olum

eH

eigh

t10 8 6 4 2

13 11 9 7 5

130

176

162

112 50

1 2 3 4 5

Sh

eet

1S

hee

t 2

Sh

eet

3

Not

ice

that

x c

ann

ot b

e gr

eate

r th

an 5

bec

ause

12

- 2

x m

ust

be

posi

tive

. In

th

is c

ase,

th

e bo

x w

ith

th

e gr

eate

st v

olu

me

is 1

76 c

ubi

c in

ches

wh

en x

= 2

.

Exam

ple

x

x

x 12 -

2x

x

15 -

2x

x

xx

xx

8-3

015_

028_

ALG

1_A

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M_C

08_C

R_6

6028

2.in

dd

2412

/20/

10

5:27

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 8-4

Cha

pte

r 8

25

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

S

pecia

l P

rod

ucts

Squ

ares

of

Sum

s an

d D

iffe

ren

ces

Som

e pa

irs

of b

inom

ials

hav

e pr

odu

cts

that

fo

llow

spe

cifi

c pa

tter

ns.

On

e su

ch p

atte

rn i

s ca

lled

th

e sq

uar

e of

a s

um

. An

oth

er i

s ca

lled

th

e sq

uar

e of

a d

iffe

ren

ce.

Sq

uar

e o

f a

Su

m(a

+ b

)2 =

(a

+ b

)(a

+ b

) =

a2

+ 2

ab +

b2

Sq

uar

e o

f a

Diff

eren

ce(a

- b

)2 =

(a

- b

)(a

- b

) =

a2

- 2

ab +

b2

F

ind

(3a

+ 4

)(3a

+ 4

).

Use

th

e sq

uar

e of

a s

um

pat

tern

, wit

h

a =

3a

and

b =

4.

(3a

+ 4

)(3a

+ 4

) =

(3a

)2 +

2(3

a)(4

) +

(4)

2

=

9a2

+ 2

4a +

16

Th

e pr

odu

ct i

s 9a

2 +

24a

+ 1

6.

F

ind

(2z

- 9

)(2z

- 9

).

Use

th

e sq

uar

e of

a d

iffe

ren

ce p

atte

rn w

ith

a

= 2

z an

d b

= 9

.(2

z -

9)(

2z -

9)

= (

2z)2

- 2

(2z)

(9)

+ (

9)(9

)

= 4

z2 -

36z

+ 8

1T

he

prod

uct

is

4z2

- 3

6z +

81.

Exer

cise

s

Fin

d e

ach

pro

du

ct.

1. (

x -

6)2

2. (3

p +

4)2

3. (4

x -

5)2

x

2 -

12x

+ 3

6 9

p2

+ 2

4p +

16

16x

2 -

40x

+ 2

5

4. (

2x -

1)2

5. (2

h +

3)2

6. (m

+ 5

)2

4

x2

- 4

x +

1

4h

2 +

12h

+ 9

m

2 +

10m

+ 2

5

7. (

a +

3)2

8. (3

- p

)2 9.

(x -

5y)

2

a

2 +

6a +

9

9 -

6p

+ p

2 x

2 -

10x

y +

25y

2

10. (

8y +

4)2

11. (

8 +

x)2

12. (

3a -

2b)

2

6

4y2

+ 6

4y +

16

64

+ 1

6x +

x2

9a

2 -

12a

b +

4b

2

13. (

2x -

8)2

14. (

x2 +

1)2

15. (

m2

- 2

)2

4

x2

- 3

2x +

64

x4

+ 2

x2

+ 1

m

4 -

4m

2 +

4

16. (

x3 -

1)2

17. (

2h2

- k

2 )2

18.

( 1 −

4 x

+ 3

) 2

x

6 -

2x

3 + 1

4

h4

- 4

h2 k

2 +

k4

1

−

16 x

2 +

3 −

2 x

+ 9

19. (

x -

4y2 )

2 20

. (2p

+ 4

r)2

21.

( 2 −

3 x

- 2

) 2

x

2 -

8xy

2 +

16y

4 4

p2

+ 1

6pr

+ 1

6r2

4 −

9 x

2 -

8 −

3 x

+ 4

Exam

ple

1Ex

amp

le 2

8-4

015_

028_

ALG

1_A

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M_C

08_C

R_6

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2.in

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/20/

10

5:27

PM

Answers (Lesson 8-3 and Lesson 8-4)

A01_A14_ALG1_A_CRM_C08_AN_660282.indd A11A01_A14_ALG1_A_CRM_C08_AN_660282.indd A11 12/20/10 9:37 PM12/20/10 9:37 PM

Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 8

26

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

(co

nti

nu

ed)

Sp

ecia

l P

rod

ucts

Exam

ple

Pro

du

ct o

f a

Sum

an

d a

Dif

fere

nce

Th

ere

is a

lso

a pa

tter

n f

or t

he

prod

uct

of

a su

m a

nd

a di

ffer

ence

of

the

sam

e tw

o te

rms,

(a

+ b

)(a

- b

). T

he

prod

uct

is

call

ed t

he

dif

fere

nce

of

squ

ares

.

Pro

du

ct o

f a

Su

m a

nd

a D

iffer

ence

(a +

b)(

a -

b)

= a

2 -

b2

F

ind

(5x

+ 3

y)(5

x -

3y)

.

(a

+ b

)(a

- b

) =

a2

- b

2 P

rodu

ct o

f a

Sum

and

a D

iffer

ence

(5x

+ 3

y)(5

x -

3y)

= (

5x)2

- (

3y)2

a =

5x

and

b =

3y

= 2

5x2

- 9

y2 S

impl

ify.

Th

e pr

odu

ct i

s 25

x2 -

9y2 .

Exer

cise

sF

ind

eac

h p

rod

uct

.

1. (

x -

4)(

x +

4)

2. (

p +

2)(

p -

2)

3. (

4x -

5)(

4x +

5)

x

2 -

16

p2

- 4

1

6x2

- 2

5

4. (

2x -

1)(

2x +

1)

5. (

h +

7)(

h -

7)

6. (

m -

5)(

m +

5)

4

x2

- 1

h

2 -

49

m2

- 2

5

7. (

2d -

3)(

2d +

3)

8. (

3 -

5q)

(3 +

5q)

9.

(x

- y

)(x

+ y

)

4d

2 -

9

9 -

25q

2 x

2 -

y2

10. (

y -

4x)

( y +

4x)

11

. (8

+ 4

x)(8

- 4

x)

12. (

3a -

2b)

(3a

+ 2

b)

y2

- 1

6x2

64

- 1

6x2

9a

2 -

4b

2

13. (

3y -

8)(

3y +

8)

14. (

x2 -

1)(

x2 +

1)

15. (

m2

- 5

)(m

2 +

5)

9

y2

- 6

4 x

4 -

1

m4

- 2

5

16. (

x3 -

2)(

x3 +

2)

17. (

h2

- k

2 )(h

2 +

k2 )

18

. ( 1 −

4 x

+ 2

) ( 1 −

4 x

- 2

)

x

6 -

4

h4

- k

4

1 −

16

x 2

- 4

19. (

3x -

2y2 )

(3x

+ 2

y2 )

20. (

2p -

5r)

(2p

+ 5

r)

21.

( 4 −

3 x

- 2

y ) ( 4 −

3 x

+ 2

y )

9

x2

- 4

y4

4p

2 -

25r

2 16

−

9 x

2 -

4 y 2

8-4

015_

028_

ALG

1_A

_CR

M_C

08_C

R_6

6028

2.in

dd

2612

/20/

10

5:27

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 8-4

Cha

pte

r 8

27

Gle

ncoe

Alg

ebra

1

Skill

s Pr

acti

ceS

pecia

l P

rod

ucts

Fin

d e

ach

pro

du

ct.

1. (

n +

3)2

2. (x

+ 4

)(x

+ 4

)

n2

+ 6

n +

9

x2

+ 8

x +

16

31. (

y -

7)2

4. (t

- 3

)(t

- 3

)

y2

- 1

4y +

49

t2

- 6

t +

9

5. (

b +

1)(

b -

1)

6. (a

- 5

)(a

+ 5

)

b2

- 1

a

2 -

25

7. (

p -

4)2

8. (z

+ 3

)(z

- 3

)

p2

- 8

p +

16

z2

- 9

9. (

ℓ +

2)(

ℓ +

2)

10. (

r -

1)(

r -

1)

ℓ

2 +

4ℓ +

4

r2

- 2

r +

1

11. (

3g +

2)(

3g -

2)

12. (

2m -

3)(

2m +

3)

9

g2

- 4

4

m2

- 9

13. (

6 +

u)2

14. (

r +

t)2

3

6 +

12u

+ u

2 r

2 +

2rt

+ t

2

15. (

3q +

1)(

3q -

1)

16. (

c -

d)2

9

q2

- 1

c

2 -

2cd

+ d

2

17. (

2k -

2)2

18. (

w +

3h

)2

4

k2

- 8

k +

4

w2

+ 6

wh

+ 9

h2

19. (

3p -

4)(

3p +

4)

20. (

t +

2u

)2

9

p2

- 1

6 t

2 +

4tu

+ 4

u2

21. (

x -

4y)

2 22

. (3b

+ 7

)(3b

- 7

)

x2

- 8

xy +

16y

2 9

b2

- 4

9

23. (

3y -

3g)

(3y

+ 3

g)

24. (

n2

+ r

2 )2

9

y2

- 9

g2

n4

+ 2

n2 r

2 +

r 4

25. (

2k +

m2 )

2 26

. (3t

2 -

n)2

4

k2

+ 4

km

2 +

m4

9t4

- 6

t2 n +

n2

27. G

EOM

ETRY

Th

e le

ngt

h o

f a

rect

angl

e is

th

e su

m o

f tw

o w

hol

e n

um

bers

. Th

e w

idth

of

the

rect

angl

e is

th

e di

ffer

ence

of

the

sam

e tw

o w

hol

e n

um

bers

. Usi

ng

thes

e fa

cts,

wri

te a

ve

rbal

exp

ress

ion

for

th

e ar

ea o

f th

e re

ctan

gle.

Th

e ar

ea is

th

e sq

uar

e o

f th

e la

rger

nu

mb

er m

inu

s th

e sq

uar

e o

f th

e sm

alle

r n

um

ber

.

8-4

015_

028_

ALG

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M_C

08_C

R_6

6028

2.in

dd

2712

/20/

10

5:27

PM

Answers (Lesson 8-4)


Co

pyr

ight

© G

lenc

oe/

McG

raw

-Hill

, a d

ivis

ion

of

The

McG

raw

-Hill

Co

mp

anie

s, In

c.

An

swer

s

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 8

28

Gle

ncoe

Alg

ebra

1

Prac

tice

S

pecia

l P

rod

ucts

Fin

d e

ach

pro

du

ct.

1. (

n +

9)2

2. (q

+ 8

)2 3.

(x -

10)

2

n

2 +

18n

+ 8

1 q

2 +

16q

+ 6

4 x

2 -

20x

+ 1

00

4. (

r -

11)

2 5.

( p

+ 7

)2 6.

(b +

6)(

b -

6)

r

2 -

22r

+ 1

21

p2

+ 1

4p +

49

b2

- 3

6

7. (

z +

13)

(z -

13)

8.

(4j

+ 2

)2 9.

(5w

- 4

)2

z

2 -

169

1

6j2

+ 1

6j +

4

25w

2 -

40w

+ 1

6

10. (

6h -

1)2

11. (

3m +

4)2

12. (

7v -

2)2

3

6h2

- 1

2h +

1

9m

2 +

24m

+ 1

6 4

9v2

- 2

8v +

4

13. (

7k +

3)(

7k -

3)

14. (

4d -

7)(

4d +

7)

15. (

3g +

9h

)(3g

- 9

h)

4

9k2

- 9

1

6d2

- 4

9 9

g2

- 8

1h2

16. (

4q +

5t)

(4q

- 5

t)

17. (

a +

6u

)2 18

. (5r

+ p

)2

1

6q2

- 2

5t2

a2

+ 1

2au

+ 3

6u2

25r

2 +

10r

p +

p2

19. (

6h -

m)2

20. (

k -

6y)

2 21

. (u

- 7

p)2

3

6h2

- 1

2hm

+ m

2 k

2 -

12k

y +

36y

2 u

2 -

14u

p +

49p

2

22. (

4b -

7v)

2 23

. (6n

+ 4

p)2

24. (

5q +

6t)

2

1

6b2

- 5

6bv +

49v

2 3

6n2

+ 4

8np

+ 1

6p2

25q

2 +

60q

t +

36t

2

25. (

6a -

7b)

(6a

+ 7

b)

26. (

8h +

3d

)(8h

- 3

d)

27. (

9x +

2y2 )

2

3

6a2

- 4

9b2

64h

2 -

9d

2 8

1x2

+ 3

6xy

2 +

4y

4

28. (

3p3

+ 2

m)2

29. (

5a2

- 2

b)2

30. (

4m3

- 2

t)2

9

p6

+ 1

2p3 m

+ 4

m2

25a

4 -

20a

2 b +

4b

2 1

6m6

- 1

6m3 t

+ 4

t2

31. (

6b3

- g

)2 32

. (2b

2 -

g)(

2b2

+ g

) 33

. (2v

2 +

3x2 )

(2v2

+ 3

x2 )

36b

6 -

12b

3 g +

g2

4b

4 -

g2

4v

4 +

12v

2 x2

+ 9

x4

34. G

EOM

ETRY

Jan

elle

wan

ts t

o en

larg

e a

squ

are

grap

h t

hat

sh

e h

as m

ade

so t

hat

a s

ide

of t

he

new

gra

ph w

ill

be 1

in

ch m

ore

than

tw

ice

the

orig

inal

sid

e g.

Wh

at t

rin

omia

l re

pres

ents

th

e ar

ea o

f th

e en

larg

ed g

raph

? 4g

2 +

4g

+ 1

35. G

ENET

ICS

In a

gu

inea

pig

, pu

re b

lack

hai

r co

lori

ng

B i

s do

min

ant

over

pu

re w

hit

e co

lori

ng

b. S

upp

ose

two

hyb

rid

Bb

guin

ea p

igs,

wit

h b

lack

hai

r co

lori

ng,

are

bre

d.

a. F

ind

an e

xpre

ssio

n f

or t

he

gen

etic

mak

e-u

p of

th

e gu

inea

pig

off

spri

ng.

0.

25B

B +

0.5

0Bb

+ 0

.25b

b

b.

Wh

at i

s th

e pr

obab

ilit

y th

at t

wo

hyb

rid

guin

ea p

igs

wit

h b

lack

hai

r co

lori

ng

wil

l pr

odu

ce a

gu

inea

pig

wit

h w

hit

e h

air

colo

rin

g? 2

5%

8-4

015_

028_

ALG

1_A

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M_C

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R_6

6028

2.in

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/20/

10

5:27

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 8-4

Cha

pte

r 8

29

Gle

ncoe

Alg

ebra

1

1. P

RO

BA

BIL

ITY

Th

e sp

inn

er b

elow

is

divi

ded

into

2 e

qual

sec

tion

s. I

f yo

u s

pin

th

e sp

inn

er 2

tim

es i

n a

row

, th

e po

ssib

le

outc

omes

are

sh

own

in

th

e ta

ble

belo

w.

BLUE

RED

red

red

blue

red

red

blue

blue

blue

W

hat

is

the

prob

abil

ity

of s

pin

nin

g a

blu

e an

d a

red

in t

wo

spin

s?

50%

2. G

RA

VIT

Y T

he

hei

ght

of a

pen

ny

t se

con

ds a

fter

bei

ng

drop

ped

dow

n a

wel

l is

giv

en b

y th

e pr

odu

ct o

f (1

0 –

4t)

and

(10

+ 4

t). F

ind

the

prod

uct

an

d si

mpl

ify.

W

hat

typ

e of

spe

cial

pro

duct

doe

s th

is

repr

esen

t?10

0 -

16t

2 ; p

rod

uct

of

a su

m a

nd

d

iffer

ence

3. T

RA

FFIC

PLA

NN

ING

Th

e L

inco

ln

Mem

oria

l in

Was

hin

gton

, D.C

., is

su

rrou

nde

d by

a c

ircu

lar

driv

e ca

lled

L

inco

ln C

ircl

e. S

upp

ose

the

Nat

ion

al

Par

k S

ervi

ce w

ants

to

chan

ge t

he

layo

ut

of L

inco

ln C

ircl

e so

th

at t

her

e ar

e tw

o co

nce

ntr

ic c

ircu

lar

road

s. W

rite

a

poly

nom

ial

equ

atio

n f

or t

he

area

A o

f th

e sp

ace

betw

een

th

e ro

ads

if t

he

radi

us

of

the

insi

de r

oad

is 1

0 m

eter

s le

ss t

han

th

e ra

diu

s of

th

e ou

tsid

e ro

ad.

A

= 2

0πr

- 1

00π

Linc

oln

Mem

oria

l

4. B

USI

NES

S T

he

Com

bo L

ock

Com

pan

y fi

nds

th

at i

ts p

rofi

t da

ta f

rom

200

5 to

th

e pr

esen

t ca

n b

e m

odel

ed b

y th

e fu

nct

ion

y

= 4

n2

+ 4

4n+

121

, wh

ere

y is

th

e pr

ofit

n

yea

rs s

ince

200

5. W

hic

h s

peci

al

prod

uct

doe

s th

is p

olyn

omia

l de

mon

stra

te?

Exp

lain

.sq

uar

e o

f a

sum

; it

can

als

o b

e w

ritt

en a

s (2

n+

11)

2

5. S

TOR

AG

E A

cyl

indr

ical

tan

k is

pla

ced

alon

g a

wal

l. A

cyl

indr

ical

PV

C p

ipe

wil

l be

hid

den

in

th

e co

rner

beh

ind

the

tan

k.

See

th

e si

de v

iew

dia

gram

bel

ow. T

he

radi

us

of t

he

tan

k is

r i

nch

es a

nd

the

radi

us

of t

he

PV

C p

ipe

is s

in

ches

.

Wal

lTa

nk

Pipe

Floo

r

r - s

r + s r -

s

a. U

se t

he

Pyt

hag

orea

n T

heo

rem

to

wri

te a

n e

quat

ion

for

th

e re

lati

onsh

ip

betw

een

th

e tw

o ra

dii.

Sim

plif

y yo

ur

equ

atio

n s

o th

at t

her

e is

a z

ero

on o

ne

side

of

the

equ

als

sign

.

0 =

r2

- 6

rs +

s2

b.

Wri

te a

pol

ynom

ial

equ

atio

n y

ou c

ould

so

lve

to f

ind

the

radi

us

s of

th

e P

VC

pi

pe i

f th

e ra

diu

s of

th

e ta

nk

is

20 i

nch

es.

Wor

d Pr

oble

m P

ract

ice

Sp

ecia

l P

rod

ucts

0 =

s2

- 1

20s +

40

0

8-4

029_

042_

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1_A

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M_C

08_C

R_6

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10

5:27

PM

Answers (Lesson 8-4)


Co

pyrig

ht © G

lencoe/M

cGraw

-Hill, a d

ivision o

f The M

cGraw

-Hill C

om

panies, Inc.

PDF Pass



NA

ME

DAT

E

P

ER

IOD

Cha

pte

r 8

30

Gle

ncoe

Alg

ebra

1

Enri

chm

ent

Su

ms a

nd

Dif

fere

nces o

f C

ub

es

Rec

all

the

form

ula

s fo

r fi

ndi

ng

som

e sp

ecia

l pr

odu

cts:

Per

fect

-squ

are

trin

omia

ls:

(a +

b)2

= a

2 +

2ab

+ b

2 or

(a -

b)2

= a

2 -

2ab

+ b

2 D

iffe

ren

ce o

f tw

o sq

uar

es:

(a +

b)(

a -

b)

= a

2 -

b2

A p

atte

rn a

lso

exis

ts f

or f

indi

ng

the

cube

of

a su

m (

a +

b)3 .

1. F

ind

the

prod

uct

of

(a +

b)(

a +

b)(

a +

b).

a

3 +

3a

2 b +

3ab

2 +

b3

2. U

se t

he

patt

ern

fro

m E

xerc

ise

1 to

eva

luat

e (x

+ 2

)3 .

x3

+ 6

x2

+ 1

2x +

8

3. B

ased

on

you

r an

swer

to

Exe

rcis

e 1,

pre

dict

th

e pa

tter

n f

or t

he

cube

of

a di

ffer

ence

(a

- b

)3 .

a3

- 3

a2 b

+ 3

ab

2 -

b3

4. F

ind

the

prod

uct

of

(a -

b)(

a -

b)(

a -

b)

and

com

pare

it

to y

our

answ

er f

or E

xerc

ise

3.

a3

- 3

a2 b

+ 3

ab

2 -

b3

5. U

se t

he

patt

ern

fro

m E

xerc

ise

4 to

eva

luat

e (x

- 4

)3 .

x3

- 1

2x2

+ 4

8x -

64

Fin

d e

ach

pro

du

ct.

6. (

x +

6)3

7. (x

- 1

0)3

x

3 +

18x

2 +

108

x +

216

x

3 -

30x

2 +

30

0x -

10

00

8. (

3x -

y)3

9. (2

x -

y)3

27

x3

- 2

7x2 y

+ 9

xy

2 -

y3

8x

3 -

12x

2 y +

6xy

2 -

y3

10. (

4x +

3y)

3 11

. (5x

+ 2

)3

64

x3

+ 1

44x

2 y +

108

xy

2 +

27y

3 12

5x3

+ 1

50x

2 +

60x

+ 8

8-4

029_

042_

ALG

1_A

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M_C

08_C

R_6

6028

2.in

dd

3012

/20/

10

5:27

PM


NA

ME

DAT

E

P

ER

IOD

Lesson 8-5

Cha

pte

r 8

31

Gle

ncoe

Alg

ebra

1

Stud

y G

uide

and

Inte

rven

tion

Usin

g t

he D

istr

ibu

tive P

rop

ert

y

Use

th

e D

istr

ibu

tive

Pro

per

ty t

o F

acto

r T

he

Dis

trib

uti

ve P

rope

rty

has

bee

n u

sed

to m

ult

iply

a p

olyn

omia

l by

a m

onom

ial.

It c

an a

lso

be u

sed

to e

xpre

ss a

pol

ynom

ial

in

fact

ored

for

m. C

ompa

re t

he

two

colu

mn

s in

th

e ta

ble

belo

w.

U

se t

he

Dis

trib

uti

veP

rop

erty

to

fact

or 1

2mp

+ 8

0m2 .

Fin

d th

e G

CF

of

12m

p an

d 80

m2 .

12m

p =

2 �

2 � 3

� m

� p

80m

2 =

2 �

2 � 2

� 2

� 5

� m

� m

GC

F =

2 �

2 � m

or

4mW

rite

eac

h t

erm

as

the

prod

uct

of

the

GC

F

and

its

rem

ain

ing

fact

ors.

12m

p +

80m

2 =

4m

(3 �

p) +

4m

(2 �

2 � 5

� m

)

= 4

m(3

p) +

4m

(20m

)

= 4

m(3

p +

20m

)T

hu

s 12

mp

+ 8

0m2

= 4

m(3

p +

20m

).

F

acto

r 6a

x +

3a

y +

2bx

+ b

y b

y gr

oup

ing.

6ax

+ 3

ay +

2bx

+ b

y

= (

6ax

+ 3

ay)

+ (

2bx

+ b

y)

= 3

a(2x

+ y

) +

b(2

x +

y)

=

(3a

+ b

)(2x

+ y

)C

hec

k u

sin

g th

e F

OIL

met

hod

.(3

a +

b)(

2 x +

y)

=

3a(

2x)

+ (

3a)(

y) +

(b)

(2x)

+ (

b)(y

)

= 6

ax +

3ay

+ 2

bx +

by

�

Exer

cise

sF

acto

r ea

ch p

olyn

omia

l.

1. 2

4x +

48y

2.

30m

p2 +

m2 p

- 6

p 3.

q4

- 1

8q3

+ 2

2q

24(

x +

2y)

p(3

0mp

+ m

2 -

6)

q(q

3 -

18q

2 +

22)

4. 9

x2 -

3x

5. 4

m +

6p

- 8

mp

6. 4

5r3

- 1

5r2

3

x(3

x -

1)

2(2

m +

3p

- 4

mp

) 1

5r2 (

3r -

1)

7. 1

4t3

- 4

2t5

- 4

9t4

8. 5

5p2

- 1

1p4

+ 4

4p5

9. 1

4y3

- 2

8y2

+ y

7

t3 (2

- 6

t2 -

7t)

1

1p2 (

5 -

p2

+ 4

p3 )

y

(14y

2 -

28y

+ 1

)

10. 4

x +

12x

2 +

16x

3 11

. 4a2 b

+ 2

8ab2

+ 7

ab

12. 6

y +

12x

- 8

z

4x(1

+ 3

x +

4x

2 )

ab

(4a +

28b

+ 7

) 2

(3y +

6x -

4z)

13. x

2 +

2x

+ x

+ 2

14

. 6y2

- 4

y +

3y

- 2

15

. 4m

2 +

4m

p +

3m

p +

3p2

(

x +

1)(

x +

2)

(2y

+ 1

)(3y

- 2

) (

4m +

3p

)(m

+ p

)

16. 1

2ax

+ 3

xz +

4ay

+ y

z 17

. 12a

2 +

3a

- 8

a -

2

18. x

a +

ya

+ x

+ y

(

3x +

y)(

4a +

z)

(4a

+ 1

)(3a

- 2

) (

x +

y)(

a +

1)

Exam

ple

1Ex

amp

le 2

Mu

ltip

lyin

gFa

cto

rin

g

3(a

+ b

) =

3a

+ 3

b3a

+ 3

b =

3(a

+ b

)

x(y

- z

) =

xy

- x

zxy

- x

z =

x(y

- z

)

6y(2

x +

1)

= 6

y(2x

) +

6y(

1)

=

12x

y +

6y

12xy

+ 6

y =

6y(

2x)

+ 6

y(1)

= 6

y(2x

+ 1

)

8-5

029_

042_

ALG

1_A

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M_C

08_C

R_6

6028

2.in

dd

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/20/

10

5:27

PM

Answers (Lesson 8-4 and Lesson 8-5)


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00i ALG1 A CRM C08 TP 660282 - St. Johns County School …teachers.stjohns.k12.fl.us/santiago-alejandro-c/files/... · · 2016-12-17a. =-+ =-+ 8-4 Answers. a +) = + +-) =-+ +)(-)