2 i 3 ISPIT ZNANJA

ALGEBARSKI IZRAZI – test br.2. i 3.
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2.
( ) ( ) ( )
2 4 2 4 5 2 5 2
3 ( x ) 42x y 7 ( y )
4 5 2 4 2 4 5 5 2
c) 3x + 7y = 3x + 2⋅3⋅x ⋅7⋅ y + 7y
=
= + + =
42 ⋅
4 5 52 ⋅
= 9x + 42x y + 49y
=
= 9x + 42x y + 49y
8 4 5 10
3.
( )
2 2 2
( ) ( ) ( ) ( )
2 2
2 ( x 2x 1) 3 ( 4x 12x
9)
d) 2 x 1 3 2x 3 2 x 2 x 1 1 3 2x 2 2x
3 3
2 2 2
− − + = ⋅ − ⋅ ⋅ + − ⋅ + ⋅ ⋅ + =
= ⋅ − + − ⋅ + + =
2 2
= 2⋅x −2⋅ 2x+ 2⋅1−3⋅4x −3⋅12x−3⋅ 9 =
2
= 2x
− 4x+
2
2 12x
36x
27
2 2
= 2x −12x −4x− 36x+ 2− 27 =
=− − −
2
10x
40x
25
− − − =
2
2 4 5 2 4 5 2 4 5 2
⎛2 ⎞⎛2 ⎞ ⎛2
⎞
a) ⎜ x − 5y z ⎟⎜ x + 5y z ⎟ = ⎜ x ⎟ − ( 5y z ) =
⎝3 ⎠⎝3 ⎠ ⎝3
⎠
2
3
4
9
x 25 y z
4 4 8 10
= x −25y z
9
2
2 2 2 4 2 5 2
= ⋅( x ) −5
⋅
2
( y ) ⋅ ( z ) =
22 ⋅ 42 ⋅ 52 ⋅
= ⋅ − ⋅ ⋅ =
( )( ) ( ) ( )
b) 3x+ y−z 3x− y+ z = ⎡⎣3x+ y− z ⎤⎦⋅⎡⎣3x− y− z ⎤⎦
=
2 2
= ( 3x) −( y− z)
=
( )
2 2 2 2
= 3 ⋅x − y − 2yz+ z =
2 2 2
= 9x − y + 2yz− z =
2 2 2
= 9x − y − z + 2yz
2 2 2 2 2
( )( ) ( ) ( )
c) x− 1 x+ 1 − x+ 2 = x −1 − x + 2⋅x⋅ 2+ 2 =
2 2
= x −1−x −4x− 4 =
2 2
= x − x −4x−1− 4 =
=−4x
−5
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