# Basic Algebra Formulas

Algebraic formulas are mathematical expressions that help us understand the relationships and patterns between variables, constants, and operations. These formulas are used to solve equations, simplify expressions, and explain mathematical relationships.

Here are some basic formulas of algebra that used in various areas of mathematics and applications:

## Basic Algebra Formulas

Square formulas

• (a+b)² = a² + b² + 2ab
• (a-b)² = a² + b² – 2ab
• (a+b)² + (a-b)² = 2( a² + b² )
• (a+b)² – (a-b)² = 4ab
• a² – b² = (a-b)(a+b)
• a² + b² = (a + b)² – 2ab
• (a+b+c)² = a²+b²+c²+2ab+2ac+2bc
• (a-b-c)² = a²+b²+c²-2ab-2ac+2bc

Cube Formulas:

• (a+b)³ = a³ + b³ + 3a²b + 3ab² OR a³ + b³ + 3ab(a + b)
• (a-b)³ = a³ – 3a²b + 3ab² – b³ OR a³ – b³ – 3a²b + 3ab² OR a³ – b³ – 3ab(a – b)
• (a+b)³ + (a-b)³ = 2a³ + 6ab²
• (a+b)³ – (a-b)³ = 6a²b + 2b³
• a³ + b³ = (a + b) (a² + b² – ab)
• a³ – b³ = (a – b) (a² + b² + ab)
• (a + b + c)³ = a³ + b³ + c³ + 3a²b + 3a²c + 3ab² + 3ac² + 3bc² + 3b²c + 6abc
• a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ac)

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