### Topics of Advanced Maths with Questions:-

• Algebra
• Trigonometry
• Height & Distance
• Geometry
• Mensuration
• Coordinate Geometry

## Important Formulas & Identities

1. (a + b)^2 = a^2 + 2ab + b^2
2. (a — b)^2 = a^2 — 2ab + b^2
3. (a + b)^2 + (a — b)^2 = 2(a^2 + b^2)
4. (a + b)^2 — (a — b)^2 = 4ab
5. a2 — b2 = (a + b) (a — b)
6. (a + b)^3 = a^3 + b^3 + 3ab(a + b)
7. (a — b)^3 = a^3 b^3 3ab(a —b)
8. a^3+ b^3= (a + b)(a^2 + b^2 — ab)
9. a^3 — b^3 = (a — b)(a^2 + b^2 + ab)
10. (a + b + c)^2 = a^2 + b^2 + C^2 ± 2(ab + bc +ca)
11. a^2+ b^2 + c^2 + ab + be + ca = 1 /2[(a + b)^2 (b + c)^2 (c + a)^2]
12. a^2+ b^2+ c^2—ab—bc —ca = 1/2[(a — b)^2 + (b — c)^2 + (c — a)^2]
13. (a + b)^3 + (a — b)^3 = 2(a^3 + 3ab^2) = 2a(a^2 + 3b^2)
14. (a + b)^3 — (a — b)^3 = 2b^3+ 3a^2b)= 2b(3a^2+ b^2)
15. (a + b)^4 = a^4 + 4a^3 b + 6a^2 b^2 + 4ab^3 + b^4
16. (a — b)4 = a^4 — 4a^3 b + 6a^2 b^2 — 4ab^3+ b4
17. a^4—b^4= (a^2— b^2)(a^2+ b^2)
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