Challenge 56. Simplify (a + b + c)2.- Number Theory You can use factoring to show th a t the sum of two m ultiples of 3 is
also a m ultiple of 3.
If m and n are integers, th e n 3m and 3n are multiples of three.
3 m + 3 n = 3 (m + n)
Since m + n is an integer, 3(m + n) is a m ultiple of three.
a. Show th at if an integer is one m ore th a n a m ultiple of 3, th e n its square is also
one m ore th a n a m ultiple of 3.
b. Reasoning If an integer is two m ore th a n a m ultiple of 3, is its square also two
m ore th a n a m ultiple of 3? Explain. - The form ula V = §7rr3 gives th e volum e of a sphere w ith radius r. Find th e volum e
of a sphere w ith radius x + 3. W rite your answ er in stan d ard form.
St an d ar d i zed Test Pr ep
ySAT/ACT
Short
, R e s p o n s e
- W hat is a sim pler form of (2x + 5)(2x - 5)?
<3D 4x2 - 20x - 25 C D 4 x 2 + 20x + 25 CD 4x2 - 25 - Sara a n d Nick sold tickets to a play. Sara sold 20 stu d en t tickets an d 3 adult
tickets for m ore th a n $60. Nick sold 15 stu d e n t tickets an d 5 ad u lt tickets for
less th a n $75. This inform ation can b e re p resen te d by 20x + 3y > 60 an d
15x + 5y < 75, w here x is th e price of a stu d e n t ticket a n d y is th e price of
an adult ticket. The inequalities are grap h ed at th e right. W hich could b e the
price of a student ticket?
C D $1 C D $5.50
C D $2.75 C D $ 6
61. G raph the solutions of th e system. 5x + 4y > 20
5x + 4y < 202x — 5Ticket Sales25
20
15
10
5
0y i
Ii
K
>....
\ s. X
0 1 2 3 4 5 6Mixed Review
Simplify each product.- (3x + 2)(2x - 5) 63. (4m — l)(6m — 7)
See Lesson 8-3.- (x + 9)(5x + 8)
Find each percent change. Describe the percent change as an increase or
decrease. If necessary, round to the nearest tenth.- $4 to $3 66. 4 ft to 5 ft 67. 12 lb to 15 lb
Get Read y! To p re p a re fo r Lesson 8 - 5 , d o Exercises 6 9 - 7 1.
See Lesson 2-10.- $40 to $35
Factor each polynomial.- 12x4 + 30x3 + 42x 70. 72x + 54x + 27
See Lesson 8-2.- 35x3 + 7x2 + 63x
0
PowerAlgebra.com Lesso n 8-4 M u l t i p l yi n g Sp eci al Cases^509