Several key algebraic formulas are used for expansion in mathematics, particularly in Class 9. Here are some of the most common and important ones:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
- (a + b)(a - b) = a² - b²
- (x + a)(x + b) = x² + (a + b)x + ab
- (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
- (a + b)³ = a³ + 3a²b + 3ab² + b³ = a³ + b³ + 3ab(a + b)
- (a - b)³ = a³ - 3a²b + 3ab² - b³ = a³ - b³ - 3ab(a - b)
- a³ + b³ = (a + b)(a² - ab + b²)
- a³ - b³ = (a - b)(a² + ab + b²)
- a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)
These formulas are crucial for simplifying algebraic expressions and solving equations. Understanding and memorizing these formulas will greatly assist in tackling problems related to expansion.
