Algebraic identities or equations

  1. (x+y)(x+y) = x²+2xy+y²
  2. (x-y)(x-y) = x²-2xy+y²
  3. (x+y)(x-y) = x²-y²
  4. (x+a)(x+b) = x²+(a+b)x+ab
  5. (x+y+z)² = x²+y²+z²+2xy+2xz+2yz
  6. (x+y)³ = x³+y³+3x²y+3y²x  or  x³+y³+3xy(x+y)
  7. (x-y)³ = x³-y³-3x²y+3y²x  or  x³-y³-3xy(x-y)
  8. x³+y³+z³-3xyz = (x+y+Z)(x²+y²+z²-xy-xz-yz)
  9. x³+y³ = (x+y)(x²-xy+y²)
  10. x³-y³ = (x-y)(x²+xy+y²)
  11. if x+y+z = 0 then x³+y³+z³ = 3xyz

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