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 Wzory skróconego mnożenia
Biuro Konstrukcji Elektronicznych






teraz jesteś Wzory
Wzory skróconego mnożenia
Wzory skróconego mnożenia
Dla dowolnych liczb całkowitych dodatnich  n,\: k  oraz dowolnych liczb rzeczywistych  a,\:b,\:c  zachodzą wzory:
 
DWUMIAN NEWTONA

{\Large (a+b)^n\:=\: \sum_{k=0}^{n}{{n}\choose{k}} a^{\small n-k}\; {\large b^{\small k} } }

(a+b)^n\:=\: {{n}\choose{0}} a^n \:+\: {{n}\choose{1}} a^{n-1} b \:+\: ... \:+\: {{n}\choose{k}} a^{n-k} b^k \:+\: ... \:+\: {{n}\choose{n-1}} a b^{n-1} \:+\: {{n}\choose{n}} b^n.
W szczególności:


 (a+b)^2\:=\: a^2\:+\:2ab \:+\:b^2
kwadrat sumy
 (a-b)^2\:=\: a^2\:-\:2ab \:+\:b^2 kwadrat różnicy
 (a+b)^3\:=\: a^3\:+\:3a^2b \:+\:3ab^2\:+\:b^3 sześcian sumy
 (a-b)^3\:=\: a^3\:-\:3a^2b \:+\:3ab^2\:-\:b^3 sześcian różnicy
a^n-b^n\:=\: (a-b)(a^{n-1}\:+\:a^{n-2}b\:+\: ... \:+\: a^{n-k}b^k\:+\: ... \:+\:ab^{n-2}\:+\:b^{n-1}).
W szczególności:


 a^2-b^2\:=\: (a-b)(a+b)
różnica kwadratów
 a^3-b^3\:=\: (a-b)(a^2+ab+b^2) różnica sześcianów
 a^3+b^3\:=\: (a+b)(a^2-ab+b^2) suma sześcianów
(a+b+c)^2\:=\: a^2+b^2+c^2+2ab+2bc+2ca.
cron