2 i 3 ISPIT ZNANJA

ALGEBARSKI IZRAZI – test br.2. i 3.
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19.
3 2 3 2 3
a) a − 9a + 27a− 27 = a −3⋅3⋅ a + 3⋅9⋅a− 3 =
( )
3 2 2 3
= a − ⋅a ⋅ a+ ⋅a⋅ − = a−
3 3 3 3 3
↓ ↓↓ ↓ ↓↓↓ ↓ ↑ ↑
( )
3 2 2 3
a −3⋅a ⋅ b+ 3⋅a⋅b − b = a−b
ili drugi način:
3 2 3 2 3
a − 9a + 27a− 27 = a − 9a + 27a− 3 =
3 3
= a −3 −9⋅a⋅ a+ 3⋅9⋅ a =
2 2
( a 3) ( a a 3 3 ) 9a ( a 3)
2
= ( a−3) ⋅ ( a + 3a+ 9− 9a)
=
2
= ( a −3) ⋅ ( a + 3a− 9a+ 9)
=
2
= ( a−3) ⋅( a − 6a+ 9)
=
= − ⋅ + ⋅ + − ⋅ − =
( a 3) ( a 3) ( a 3)
( a 3)
1 2 1+
2
= − ⋅ − = − =
= −
3
3
3
3 3 2 2 2 3 3 3 3 2 2 2 3 3
b) 27ab − 54abc+ 36abc − 8c = 3⋅a ⋅b −329 ⋅ ⋅ ⋅a ⋅b ⋅ c+ 334 ⋅ ⋅ ⋅abc ⋅ ⋅ −2⋅ c =
ili drugi način:
2 2 2 2 2
( 3 ab) 3 3 a b 2 c 3 3 ab2 c ( 2 c)
( 3ab) 3 ( 3ab) 2c 3 3ab ( 2c) ( 2c)
( 3ab
2c)
3 3
= ⋅ ⋅ − ⋅ ⋅ ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ ⋅ − ⋅ =
3 2 2 3
= − ⋅ ⋅ + ⋅ ⋅ − =
= −
ab − abc+ abc − c = ⋅a ⋅b − ⋅c − ⋅ ⋅aabbc ⋅ ⋅ ⋅ ⋅ + ⋅ ⋅abcc
⋅ ⋅ ⋅ =
3 3 2 2 2 3 3 3 3 3 3
27 54 36 8 3 2 3 18 2 18
3
3 3
( 3ab) ( 2c) 18 a b c ( 3 a b 2 c)
= − − ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ − ⋅ =
2 2
( ) ( )
( ) ( ) ( )
= 3ab −2c ⋅ 3ab + 3ab⋅ 2c + 2c −18abc⋅ 3ab −2c
2 2 2
( 3ab 2c) ( 9a b 6abc 4c 18abc)
= − ⋅ + + − =
(
2
) =
(
2 2
)
2
= ( 3ab −2c) ⋅ ( 3ab)
− 12abc
+( 2c)
( 3ab 2c) ( 3ab) 2 3ab 2c ( 2c)
= − ⋅ − ⋅ ⋅ + =
( 3ab 2c) ( 3ab 2c)
1 2
= − ⋅ − =
+
( 3ab 2c) ( 3ab 2c)
1 2 3
= − = −
=
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