Question

Write minimum 10 examples to show the use of algebra in creating the mathematical formulas.

Answer 1

Answer:

1. a2 – b2 = (a – b)(a + b)

2. (a + b)2 = a2 + 2ab + b2

3. a2 + b2 = (a + b)2 – 2ab

4. (a – b)2 = a2 – 2ab + b2

5. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

6. (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca

7. (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)

8. (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)

9. a3 – b3 = (a – b)(a2 + ab + b2)

10. a3 + b3 = (a + b)(a2 – ab + b2)

11. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

12. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4

13. a4 – b4 = (a – b)(a + b)(a2 + b2)

14. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

Hope it will help you