1. \((a ± b)^2 = a^2 ± 2ab + b^2\)

2. \((a + b)^2 – (a – b)^2 = 4ab\)

3. \((a + b)^2 + (a – b)^2 = 2 (a^2+ b^2)\)

4. \(a^2 – b^2= (a + b) (a – b)\)

5.
(1) \((a + b)^3= a^3+ b^3+ 3ab (a + b)\);
(2) \((a – b)^3= a^3– b^3– 3ab (a – b)\)

6.
(1) \(a^3+ b^3= (a + b) (a^2– ab + b^2)\) ;
(2) \(a^3– b^3= (a – b) (a^2+ ab + b^2)\)

7. \((a + b + c)^2= a^2+ b^2+ c^2+ 2ab + 2bc + 2ac\)

8. \(a^3+ b^3+ c^3– 3abc = (a+b+c)(a^2+ b^2+ c^2– ab – ac – bc) ⇒ if (a + b + c) = 0\) then \(a^3+ b + c^3= 3abc.\)