list of important Algebra formulas for Maths 📘 (useful for Class 8–10, CBSE & State Boards) 2026

List of important Algebra formulas for Maths 📘

(useful for Class 8–10, CBSE & State Boards)

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🔢 Basic Algebraic Identities

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 + b)(a - b) = a^2 - b^2)

5. ((x + a)(x + b) = x^2 + x(a + b) + ab)

6. ((x - a)(x - b) = x^2 - x(a + b) + ab)

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🔢 Cube Formulas

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

8. ((a - b)^3 = a^3 - b^3 - 3ab(a - b))

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

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

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🔢 Three-Variable Identity

11. (a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca))

If
👉 (a + b + c = 0)
then
👉 (a^3 + b^3 + c^3 = 3abc)

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✖️ Factorisation Formulas

12. (x^2 + (a + b)x + ab = (x + a)(x + b))

13. (x^2 - (a + b)x + ab = (x - a)(x - b))

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➗ Exponents Laws

14. (a^m \times a^n = a^{m+n})

15. (a^m \div a^n = a^{m-n})

16. ((a^m)^n = a^{mn})

17. ((ab)^n = a^n b^n)

18. (\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n})

19. (a^0 = 1) (where (a \neq 0))

20. (a^{-n} = \frac{1}{a^n})

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📐 Linear Equation (One Variable)

21. (ax + b = 0 \Rightarrow x = -\frac{b}{a})

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📊 Quadratic Equation Formula

22. (ax^2 + bx + c = 0)

[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
]

Discriminant:
[
D = b^2 - 4ac
]

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🧮 Useful Special Values

23. ((a + b)^2 + (a - b)^2 = 2(a^2 + b^2))

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