1. a(b+c) = ab + ac

2. (a+b)^{2} = a^{2} + 2ab + b^{2}

3. (a-b)^{2} = a^{2}-2ab + b^{2}

4. (a+b)^{2} = (a-b)^{2} + 4ab

5. (a-b)^{2} = (a+b)^{2} – 4ab

6. (a-b) (a+b) = a^{2} – b^{2}

7. (a+b)^{3} = a^{3} + 3ab(a+b) + b^{3}

8. (a-b)^{3} = a^{3} – 3ab(a-b) – b^{3}

9. a^{3} + b ^{3} = (a+b) (a^{2} – ab + b^{2})

10. a^{3} – b ^{3} = (a-b) (a^{2} + ab + b^{2})

11. (a^{3} – b^{3}) / (a^{2} + ab + b^{2}) = a-b

12. (a^{3} + b^{3}) / (a^{2} – ab + b^{2}) = a+b

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