Mathematics Village

FORMULAE Algebra 1. (a + b) 2 = a 2 + b 2 + 2ab = (a - b) 2 + 4ab 2. (a- b) 2 = a 2 + b 2 - 2ab = (a + b) 2 – 4ab 3. a 2 - b 2 = (a - b) (a + b) 4. a 2 + b 2 = (a + b) 2  - 2ab = (a - b) 2 + 2ab 5. (a + b) 2 + (a- b) 2 = 2(a 2 + b 2 ) 6. (a + b) 2 – (a - b) 2 = 4ab 7. (a + b + c) 2 = a 2 + b 2 + c 2 + 2ab + 2bc + 2ca 8. a 2 + b 2 + c 2 - ab - bc - ca =1/2[(a-b) 2 + (b -c) 2 + (c- a) 2 ] 9. (a + b) 3 = a 3 + b 3 + 3ab (a + b) = a 3 + 3a 2 b + 3ab 2 + b 3 10. (a- b) 3 = a 3 - b 3 -3ab (a -b) = a 3 - 3a 2 b + 3ab 2 - b 3 11. a 3 + b 3 = (a + b) 3 - 3ab (a + b) = (a + b) (a 2 –- ab + b 2 ) 12. a 3 - b 3 = (a - b) 3 + 3ab (a- b) = (a- b) (a 2 + ab + b 2 ) 13. (a + b + c) 3 = a 3 + b 3 + c 3 + 3(a + b) (b + c) (c + a) 14. a 3 + b 3 + c 3 – 3abc = (a + b + c) (a 2 + b 2 + c 2 - ab - bc - ca) If a + b + c = 0 then a 3 + b 3 + c 3 = 3abc