ALGEBARSKI IZRAZI

M-1-Kvadrat binoma
Rješenja i kompletni postupak
34. ( ) ( )
2 2
2 2
Kvadriramo po pravilu: A+ B = A + 2⋅A⋅ B+ B i A− B = A −2⋅A⋅ B+
B
2 2
( ) ( ) ( )
58) 2ab+ 3c = 2ab + 2⋅2⋅a⋅b⋅3⋅ c + 3c
=
2 2 2 2 2
= 2 ab + 12abc+ 3 c =
= 4a b + 12abc + 9c
2 3 2 2 2 2 3 3 2
59) ab+ c = ab + 2⋅a ⋅bc ⋅ + c =
2 4
60) ( 2ab
3c
)
2 2 2
2 2 2
( ) ( ) ( )
( )
2 2 2 2 3 2
= a ⋅ b + 2a bc + c =
= ab + 2abc + c
4 2 2 3 2
− ( 2ab ) 2 2 a b 3 c ( 3c
)
2 2 2 2 2 4 2 4 2
2 a ( b ) 12ab c 3 ( c )
2 2 2 2 4 4 2
2 2⋅2 2 4 4⋅2
= 4ab − 12abc + 9c
=
= 4ab − 12abc + 9c
2 4 2 4 8
2 3 2 4 2 2 3 2 2 3 2 4 2 4 2
( ab − cd ) = ( ab) − ⋅a ⋅b⋅c ⋅ d + ( cd ) =
( a ) ( b ) 2a b c d ( c ) ( d )
61) 2
= − ⋅ ⋅ ⋅ ⋅ ⋅ + =
= − + =
2 2 3 2 2 3 2 4 2 2 4 2
= ⋅ − + ⋅ =
22 ⋅ 32 ⋅ 2 3 2 4 22 ⋅ 42 ⋅
= a b − 2a b c d + c d =
4 6 2 3 2
= ab −2abcd
4 4 8
( ab c ) ( ab) a b c ( c )
2 2 3 2 2 3 3 2⋅2
( a ) ( b ) 2a b c c
2 3 2 2 2 3 2 2 3 3 2 2
62) − = −2⋅ ⋅ ⋅ + =
a b 2a b c c
22 ⋅ 32 ⋅ 2 3 3 4
= − + =
= ab − 2abc + c
4 6 2 3 3 4
( ab c ) ( ab) ab c ( c )
( a ) b 6a bc 3 ( c )
3 4 2 3 2 3 4 4 2
63) − 3 = −2⋅ ⋅3⋅ + 3 =
3 2 2 3 4 2 4 2
= ⋅ − + =
a b 6a bc 9c
32 ⋅ 2 3 4 42 ⋅
= − + =
= ab − 6abc + 9c
6 2 3 4 8
+ c d
= ⋅ − + =
5 2 2 3 2 2 3 5 5 2
( ab + c) = ( ab) + 2⋅a ⋅b⋅4⋅ c + ( 4c)
=
2 3
64) 4
( a ) ( b ) 8a b c 4 ( c )
2 2 3 2 2 3 5 2 5 2
= ⋅ + + =
22 ⋅ 32 ⋅ 2 3 5 52 ⋅
= a b + 8a b c + 16c
=
= ab + 8abc + 16c
4 6 2 3 5 10
M.I.M.-Sraga -2003./2013.
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