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Reiškinių pertvarkymai

Formulės

(a + b)^2 ; (a - b)^2

  • (a + b)^2 = a^2 + 2ab + b^2
  • (a – b)^2 = a^2 – 2ab + b^2

(a + b)^3 ; (a - b)^3

  • (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
  • (a - b)^3 = a^3 – 3a^2b + 3ab^2 – b^3

a^3 + b^3 ; a^3 - b^3

  • a^3 + b^3 = (a + b)(a^2 – ab + b^2)
  • a^3 – b^3 = (a – b)(a^2 + ab + b^2)

Trinario skaidymas dauginamaisiais

  • ax^2 + bx + c = a(x – x_1)(x – x_2)

Niutono binomas

  • (a+b)^n = sum{k=0}{n}{C{matrix{2}{1}{{k}{n}}}{}a^{n-k}b^{k}}

Pavyzdžiai

  • (a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4
  • (a+b)^5 = a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5
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