Product Formulas

Posted In: Mathematics

Real numbers: a,b,c
Whole numbers: n.k

  1. $(a+b)^2=a^2+2ab+b^2$
  2. $(a-b)^2=a^2-2ab+b^2$
  3. $(a+b)^3=a^3+3a^2b+3ab^2+b^3$
  4. $(a-b)^3=a^3-3a^2b+3ab^2-b^3$
  5. $(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4$
  6. $(a-b)^4=a^4-4a^3b+6a^2b^2-4ab^3+b^4$
  7. $(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc$
  8. $(a+b+c+…)^2=a^2+b^2+c^2+…+2(ab+ac+bc+…)$
  9. Binomial Formula:
    $(a+b)^n=^nC_0a^n+^nC_1a^{n-1}b+^nC_2a^{n-2}b^2+…+^nC_{n-1}ab^{n-1}+^nC_nb^n$,
    where $^nC_k={n!}/{k!(n-k)!}$ are the binomial coefficients.

Post Tags: Algebra


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