Important formulas for Algebra in Math Class 10:
Equations
1. Linear Equation: ax + by + c = 0
2. Quadratic Equation: ax^2 + bx + c = 0
3. Formula for solving quadratic equations: x = (-b ± √(b^2 - 4ac)) / 2a
Algebraic Expressions
1. Addition of algebraic expressions: (a + b) + (c + d) = a + b + c + d
2. Subtraction of algebraic expressions: (a + b) - (c + d) = a + b - c - d
3. Multiplication of algebraic expressions: (a + b)(c + d) = ac + ad + bc + bd
Identities
1. a^2 - b^2 = (a + b)(a - b)
2. a^3 + b^3 = (a + b)(a^2 - ab + b^2)
3. a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Inequalities
1. Linear inequality: ax + by + c > 0 (or < 0, ≥ 0, ≤ 0)
2. Quadratic inequality: ax^2 + bx + c > 0 (or < 0, ≥ 0, ≤ 0)
Formulae for special products
1. (a + b)^2 = a^2 + 2ab + b^2
2. (a - b)^2 = a^2 - 2ab + b^2
3. (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
4. (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
These formulas are essential for solving algebraic problems in Class 10 Math. Make sure to practice using them to become proficient!
