Chapter Review
97
3. a. ~ + 25 Prime; the sum of two squares does not
factor.
b. ~ + 729 = (x + 9)(~
cubes a = x, b = 9
-
9x + 81) Sum of two
C. x4 + 16 Prime; the sum of two squares does not
factor.
d. x6- 729
=(x3 - 27)(x3 + 27) Differenceof two squares
=(x - 3)(x2 + 3x + 9)(x + 3)(x2 - 3x + 9)
Difference and sum of
two cubes, a = x,b = 3
e. x6+ 512= (~+ 8)(x4- ~ + 64) Sumof two
cubesa=~,b=8
Section6.5
1. a. l
+ 125 = (y + 5)(1- 5y + 25) Sum of two
a = y, b = 5
cubes
b. 27- 8x3= (3 - 2x)(9 + 6x + 4~) Difference of
two cubes a = 3, b = 2x
C. x3
- 216 = (x -
two cubes a
6)(~ + 6x + 36) Difference of
= x, b = 6
d. 1000; + 1 = (IOz+ 1)(100; -lOz + I) Sum
of two cubes a = lOz, b = 1
e. x6 -l = (x2 - y)(x4 + ~y + I)
two cubes a =~, b = y
Difference of
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