Factors and Products Formulas

  1. $${(a + b)^2} = {a^2} + 2ab + {b^2}$$
  2. $${(a – b)^2} = {a^2} – 2ab + {b^2}$$
  3. $${(a + b)^2} = {(a – b)^2} + 4ab$$
  4. $${(a – b)^2} = {(a + b)^2} – 4ab$$
  5. $${(a + b)^2} + {(a – b)^2} = 2{a^2} + 2{b^2}$$
  6. $${(a + b + c)^2} = {a^2} + {b^2} + {c^2} + 2ab + 2bc + 2ac$$
  7. $${(a + b + c + \cdots )^2} = {a^2} + {b^2} + {c^2} + \cdots + 2(ab + ac + bc + \cdots )$$
  8. $${(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3} = {a^3} + {b^3} + 3ab(a + b)$$
  9. $${(a – b)^3} = {a^3} – 3{a^2}b + 3a{b^2} – {b^3} = {a^3} – {b^3} – 3ab(a – b)$$
  10. $$(a + b)(a – b) = {a^2} – {b^2}$$
  11. $${a^3} – {b^3} = (a – b)({a^2} + ab + {b^2})$$
  12. $${a^3} + {b^3} = (a + b)({a^2} – ab + {b^2})$$
  13. $$(a + b)(a + c) = {a^2} + (b + c)a + bc$$
  14. $$(x + b)(x + c) = {x^2} + (b + c)x + bc$$
  15. $$(a + b + c)({a^2} + {b^2} + {c^2} – ac – bc – ca) = {a^3} + {b^3} + {c^3} – 3abc$$
  16. $${a^n} – {b^n} = (a – b)({a^{n – 1}} + {a^{n – 2}}b + {a^{n – 3}}{b^2} + \cdots + {b^{n – 1}})$$ if $$n$$ is odd.
  17. $${a^n} – {b^n} = (a + b)({a^{n – 1}} – {a^{n – 2}}b + {a^{n – 3}}{b^2} – \cdots – {b^{n – 1}})$$ if $$n$$ is even.
  18. $${a^n} + {b^n} = (a + b)({a^{n – 1}} – {a^{n – 2}}b + {a^{n – 3}}{b^2} – \cdots – {b^{n – 1}})$$ if $$n$$ is odd.
  19. $$(x + a)(x + b)(x + c) = {x^3} + (a + b + c){x^2} + (ab + bc + ac)x + abc$$