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- \( (a + b)^2 = a^2 + 2ab + b^2 \)
- \( (a - b)^2 = a^2 - 2ab + b^2 \)
- \( a^2 - b^2 = (a + b)(a - b) \)
- \( a^2+b^2 = (a + b)^2 - 2ab \)
- \( a^2+b^2 = (a - b)^2 + 2ab \)
- \( (a + b)^2 = (a - b)^2+4ab \)
- \( (a - b)^2 = (a + b)^2-4ab \)
- \( ab = (\frac{a + b}{2})^2 - (\frac{a - b}{2})^2 \)
- \( (x + a)(x + b) = x^2 + (a + b)x + ab \)
- \( (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca \)
- \( a^2+b^2+c^2 = (a+b+c)^2 - 2(ab+bc+ca) \)
- \( 2(ab+bc+ca = (a+b+c)^2 - a^2+b^2+c^2 \)