data/knowledge_base/algebra.md

Algebra – Core Concepts (JEE Level)

Linear Equations

ax + b = 0
Solution: x = −b / a, where a ≠ 0

Quadratic Expressions

Standard form: ax² + bx + c

Identities

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

Inequalities

• Multiplying/dividing by a negative reverses the sign
• Check solution intervals carefully

Common Mistakes

• Cancelling terms incorrectly
• Ignoring restrictions on variables