ALGEBARSKI IZRAZI
kvadrat zbroja - MIM-Sraga
kvadrat zbroja - MIM-Sraga
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M-1-Kvadrat binoma<br />
Rješenja i kompletni postupak<br />
34. Kvadriramo po pravilu: A+ B = A + 2⋅A⋅ B+ B i A− B = A −2⋅A⋅ B+<br />
B<br />
To pravilo možemo pisati i ovako:<br />
( ) ( )<br />
2 2 2<br />
23) 3x+ 2 = 3x + 2⋅3x⋅ 2+ 2 =<br />
2 2<br />
3 x 12x<br />
4<br />
= + + =<br />
= x + x+<br />
2<br />
9 12 4<br />
( ) ( )<br />
2 2 2 2 2 2<br />
( ) i ( )<br />
2 2 2 2 2<br />
I + II = I + 2⋅I ⋅ II + II I − II = I −2⋅I ⋅ II + II<br />
2<br />
( ) ( )<br />
2 2 2<br />
24) 2x+ 5 = 2x + 2⋅2x⋅ 5+ 5 =<br />
2 2<br />
2 x 20x<br />
25<br />
= + + =<br />
= x + x+<br />
2<br />
4 20 25<br />
Sve ove zadatke možemo rješavati u jednom redu ali tada je teško pisati upute,<br />
kada svaki korak pišem u novi red tada desno od zadatka ima mjesta za uputu.<br />
2 2<br />
( a− b) = ( a)<br />
− ⋅ a⋅ b+( )<br />
25) 2 5 2 2 2 5<br />
2 2 2 2 2 2 2<br />
5b = 2 a − 20ab+ 5 b = 4a − 20ab+<br />
25b<br />
Još jednom isti zadatak:<br />
2 2 2<br />
( 2 5 ) ( 2 ) 2 2 5 ( 5 ) Primjeni: ( )<br />
2 2 2 2<br />
= − + =<br />
2 a 20ab 5 b<br />
= 4a − 20ab+<br />
25b<br />
2 2<br />
n n n<br />
a− b = a − ⋅ a⋅ b+ b = ab = a b<br />
( x y) ( x) x y ( y)<br />
2 2 2<br />
26) 2 + 3 = 2 + 2⋅2 ⋅ 3 + 3 =<br />
2 2 2 2<br />
= + + =<br />
2 x 12xy 3 y<br />
= 4x + 12xy+<br />
9y<br />
2 2<br />
2 2<br />
( x+ y) = ( x)<br />
+ ⋅ x 2y ( 2y)<br />
27) 5 2 5 2 5<br />
2 2 2 2<br />
= x + xy+ y =<br />
5 20 2<br />
= 25x + 20xy+<br />
4y<br />
2 2<br />
2<br />
⋅ + =<br />
( x y) ( x) x y ( y)<br />
2 2 2<br />
28) 3 + 4 = 3 + 2⋅3 ⋅ 4 + 4 =<br />
2 2 2 2<br />
= x + xy+ y =<br />
3 24 4<br />
= 9x + 24xy+<br />
16y<br />
2 2<br />
M.I.M.-Sraga -2003./2013.<br />
www.mim-sraga.com<br />
6<br />
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mim-sraga@zg.htnet.hr<br />
tel-01-4578-431
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