ALGEBARSKI IZRAZI

M-1-Kvadrat binoma
Rješenja i kompletni postupak
2 2 2 2 2
2
34. Kvadriramo po pravilu: ( A+ B) = A + 2⋅A⋅ B+ B i ( A− B)
= A −2⋅A⋅ B+
B
n+ n− n+ n+ n− n−
( ) ( ) ( )
1 2 2 1 2 1 2 2 2
88) 2 − 2 = 2 −2⋅2 ⋅ 2 + 2 =
( n ) 1 n+ 1 n−2
( n )
+ 1 ⋅2 −2 ⋅2
= 2 −2 ⋅2 ⋅ 2 + 2 =
( n ) 1+ n+ 1+ n−2
( n )
2⋅ + 1 2⋅ −2
= 2 − 2 + 2 =
n
2
( 2 )
2n
2
2
( 2 )
n+ 1
4
n
2
( 2 )
n−2
4
+ 1 n−2
= − + =
= − + =
= 4 − 4 + 4
n+ 1 n n−2
89)
n n+ 1 2 n 2 n n+ 1 n+
1 2
( a + a ) = ( a ) + 2⋅a ⋅ a + ( a ) =
( n )
n⋅ 2 n+ n+
1 + 1 ⋅2
= a + 2⋅ a + a =
= a + 2a + a
2n 2n+ 1 2n+
1
n− n+ n− n− n+ n+
( a a ) ( a ) a a ( a )
1 1 2 1 2 1 1 1 2
90) − = −2⋅ ⋅ + =
( n ) n−+ 1 n+
1 ( n )
−1 ⋅ 2 + 1 ⋅2
= a −2⋅ a + a =
= a − 2a + a
2n− 2 2n 2n+
2
x x x x x x
( a b ) ( a ) a b ( b )
2
2
2 x x x 2 x
= 2 ( a ) −12⋅a ⋅ b + 3 ( b )
2 2 2
91) 2 − 3 = 2 −2⋅2⋅ ⋅3⋅ + 3 =
x⋅2 x x x⋅2
= a − a b + b =
4 12 9
= 4a −12a b 9b
2x x x 2x
x y x x y y
( a b ) ( a ) a b ( b )
2 x 2 x y 2 y 2
= 2 ( a ) + 12a b + 3 ( b ) =
2 2 2
+ = + ⋅ ⋅ + =
92) 2 3 2 2 2 3 3
x⋅2 x y y⋅2
= a + a b + b =
4 12 9
= 4a + 12a b + 9b
2x x y 2y
=
M.I.M.-Sraga -2003./2013.
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