Tic
3
Formule de calcul prescurtat ( a +b) 2 =a 2 +2 ab +b 2 =a∗a+ 2∗a∗b+b∗b . ( a−b ) 2 =a 2 −2 ab + b 2 =a∗a−2∗a∗b+b∗b . a 2 −b 2 =( a−b)( a+b )=( a−b)∗( a+b) . ( a+ b+c) 2 =a 2 + b 2 +c 2 +2 ab +2 ac+ 2 bc=a∗a +b∗b+c∗c +2∗a∗b+ 2∗a∗c+2∗b∗c. ( a−b−c ) 2 =a 2 + b 2 +c 2 −2 ab−2 ac −2 bc=a∗a + b∗b+ c∗c− 2∗a∗b− 2∗a∗c− 2∗b∗c . ( a +b) 3 =a 3 +3 a 2 b +3 ab 2 +b 3 =a∗a∗a +3∗a∗a∗b+ 3∗a∗b∗b+b∗b∗b . ( a−b ) 3 =a 3 −3 a 2 b+ 3 ab 2 −b 3 =a∗a∗a−3∗a∗a∗b+3∗a∗b∗b−b∗b∗b. a 3 +b 3 + c 3 =( a+b+ c) 3 −3 ( a+ b)( b+c )( a+c ) =( a+ b+c ) ∗( a+b +c)∗( a+b+ c) −3∗( a +b)∗( b+c ) ∗( a+ c) . a 3 +b 3 =( a +b) ¿ . a 3 −b 3 =( a+b ) ( a 2 +ab + b 2 ) =( a+b )∗( a∗a + a∗b+ b∗b). a 4 +b 4 =(a 2 +b 2 − √ 2 ab )( a 2 + b 2 + √ 2 ab ) =( a∗a+ b ∗b− √ 2∗a∗b ) ∗( a∗a +b∗b+ √ 2∗a∗b ). a 4 −b 4 =( a−b)( a+b ) ( a 2 +b 2 )=( a−b)∗( a + b)∗( a∗a+b∗b ). 4 ab =( a+ b) 2 −( a−b) 2 =( a + b)∗( a+b )−( a−b)∗( a−b ) .
description
TIC
Transcript of Tic
Formule de calcul prescurtat
(a+b )2=a2+2ab+b2=a∗a+2∗a∗b+b∗b.
(a−b )2=a2−2ab+b2=a∗a−2∗a∗b+b∗b.
a2−b2= (a−b ) (a+b )=(a−b )∗(a+b).
(a+b+c )2=a2+b2+c2+2ab+2ac+2bc=a∗a+b∗b+c∗c+2∗a∗b+2∗a∗c+2∗b∗c.
(a−b−c )2=a2+b2+c2−2ab−2ac−2bc=a∗a+b∗b+c∗c−2∗a∗b−2∗a∗c−2∗b∗c.
(a+b )3=a3+3a2b+3ab2+b3=a∗a∗a+3∗a∗a∗b+3∗a∗b∗b+b∗b∗b.
(a−b )3=a3−3a2b+3ab2−b3=a∗a∗a−3∗a∗a∗b+3∗a∗b∗b−b∗b∗b.
a3+b3+c3=(a+b+c )3−3 (a+b ) (b+c ) (a+c )=(a+b+c )∗(a+b+c )∗(a+b+c )−3∗(a+b )∗(b+c )∗(a+c )
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a3+b3=(a+b ) ¿.
a3−b3=(a+b ) (a2+ab+b2 )= (a+b )∗(a∗a+a∗b+b∗b).
a4+b4=(a2+b2−√2ab ) (a2+b2+√2ab )=(a∗a+b∗b−√2∗a∗b )∗(a∗a+b∗b+√2∗a∗b).
a4−b4=(a−b ) (a+b ) (a2+b2 )=(a−b )∗(a+b )∗(a∗a+b∗b).
4 ab=(a+b )2−(a−b )2=(a+b )∗(a+b )−(a−b )∗(a−b).
NUME NR. ABSENȚE MOTIVATEAndreescu Marilena 0 0Andrei Loredana 2 2Baros Diana 7 5Blidaru Alexandru 15 14Borțosu Cristina 2 2Constantin Cătălina 5 4Crăciun Olimpia 7 5Duman Nicoleta 5 5Filipescu Alina 2 2Gălbeoru Georgiana 2 1Groșaru Roxana 2 1Ilie Mirela 2 2Ion Mihnea 8 6Lixandru Albert 5 4Lungu Alexandra 8 5Marinescu Mihai 5 4Matei Diana 3 2Mucenic Bianca 4 3Neacșu Alexandra 10 10Pîrvu Ioana 7 6Popescu Andreea 2 2Spiridon Ioana 2 2Stoicescu Cristian 20 15Tatu Diana 2 1Tănase Iuliana 5 4Trandafir Mădălina 1 1Țimonea Victoria 2 0Vaporu Livia 2 1Zăvoianu Alexandra 3 2TOTAL 140 111111
