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
( x y) ( x) x y ( y)
2 2 2
35) 0,5 − 2 = 0,5 −2⋅0,5⋅ ⋅2⋅ + 2 =
2 2 2 2
= x − x+ y =
0,5 2 2
= 0, 25x − 2x+
4y
2 2
( ) ( ) ( )
2 2 2
36) 0,2m+ 0,3n = 0,2m + 2⋅0,2⋅m⋅0,3⋅ n+ 0,3n
=
0, 2 m 0,12mn 0,3 n
2 2 2 2
= + + =
= 0,04m + 0,12mn+
0,09n
2 2
2 2
2
⎛ 1⎞ 1 ⎛1⎞
37) ⎜x+ ⎟ = x + 2⋅x⋅ + ⎜ ⎟ =
⎝ 2⎠ 2 ⎝2⎠
2
2
= x + ⋅ ⋅ x+ =
2
2
= x + x+
1 1
2 2 2
1
4
2 2
2
+ = + ⋅ ⋅ ⋅ + =
⎛3 ⎞ ⎛3 ⎞ 3
38) ⎜ x 1⎟ ⎜ x⎟
2 x 1 1
⎝2 ⎠ ⎝2 ⎠ 2
3
2
9
x
4
2
2
= x + 3x+ 1=
2
2
= + +
3x
1
2 2 2
⎛3 2 ⎞ ⎛3 ⎞ 3 2 ⎛2
⎞
39) ⎜ x+ y⎟ = ⎜ x⎟ + 2⋅ ⋅x⋅ ⋅ y+ ⎜ y⎟
=
⎝4 3 ⎠ ⎝4 ⎠ 4 3 ⎝3
⎠
2 2
3 2 3 2 2 2
3 2 232 ⋅ ⋅
= x + 2 ⋅ ⋅ ⋅x⋅ y+ y = → drugi član⋅ 2⋅ ⋅ xy = xy = 1xy
2 2
4 4 3 3
4 3 4⋅3
9 4
= x + xy+
y
16 9
2 2
M.I.M.-Sraga -2003./2013.
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