1. \( (a + b)^2 = a^2 + 2ab + b^2 \)
    2. \( (a - b)^2 = a^2 - 2ab + b^2 \)
    3. \( a^2 - b^2 = (a + b)(a - b) \)
    4. \( a^2+b^2 = (a + b)^2 - 2ab \)
    5. \( a^2+b^2 = (a - b)^2 + 2ab \)
    6. \( (a + b)^2 = (a - b)^2+4ab \)
    7. \( (a - b)^2 = (a + b)^2-4ab \)
    8. \( ab = (\frac{a + b}{2})^2 - (\frac{a - b}{2})^2 \)
    9. \( (x + a)(x + b) = x^2 + (a + b)x + ab \)
    10. \( (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \)
    11. \( a^2+b^2+c^2 = (a+b+c)^2 - 2(ab+bc+ca) \)
    12. \( 2(ab+bc+ca = (a+b+c)^2 - a^2+b^2+c^2 \)