ALGEBARSKI IZRAZI

M-1-Kvadrat binoma
Rješenja i kompletni postupak
34. Kvadriramo po pravilu: A+ B = A + 2⋅A⋅ B+ B i A− B = A −2⋅A⋅ B+
B
To pravilo možemo pisati i ovako:
( ) ( )
2 2 2 2 2 2
( ) i ( )
2 2 2 2 2
I + II = I + 2⋅I ⋅ II + II I − II = I −2⋅I ⋅ II + II
2
( )
( )
2 2 2
17) 2 + z = 2 + 2⋅2⋅ z+ z =
= 4+ 4z+
z
2 2 2
18) z− 2 = z −2⋅z⋅ 2 + 2 =
2
= − +
2 2
( x+ y)
= x + 2 x 5y ( 5y)
19) 5
Još jednom isti zadatak:
z
2
4z
4
( ) ( )
( ) ( )
2 2 2
= x + xy+ y =
2 2
2
2 2 2 2 2 2 2 2
Primjeni pravilo:
2 2
⋅ ⋅ + =
10 5
= x + 10xy+
25y
19) x+ 5y = x + 2⋅x⋅ 5y+ 5y = x + 10xy+ 5 y = x + 10xy+
25y
i ovdje
n n n
( ) u našem slučaju: ( )
2 2 2 2
ab = a b 5y = 5 y = 25y
20) 5x− y = 5x −2⋅5x⋅ y+
y = 5 x − 10xy+ y = 25x − 10xy+
y
2 2 2 2 2 2
ili možemo pisati i ovako:
( ) ( )
2 2 2
5x− y = 5x −2⋅5x⋅ y+ y =
5 10
2 2 2
= x − xy+ y =
= 25x − 10xy+
y
2 2
( ) ( )
2 2 2
21) 7x+ y = 7x + 2⋅7x⋅ y+ y =
2 2 2
= x + xy+ y =
7 14
= 49x + 14xy+
y
2 2
2
( x y) x x y ( y)
2 2
22) − 3 = −2⋅ ⋅ 3 + 3 =
2 2 2
= x − xy+ y =
6 3
= x − 6xy+
9y
2 2
M.I.M.-Sraga -2003./2013.
www.mim-sraga.com
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