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    a3b3 Formulas and Their Applications

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    Basic Concepts
    • Algebraic equation is a polynomial equation of form P = 0
    • Polynomial equations can have multiple variables
    • Examples include 4x + 3, 7 - 2x², 4x² + 3x
    Cube Formulas
    • Difference of cubes: a3 - b3 = (a - b)(a² + ab + b²)
    • Sum of cubes: a3 + b3 = (a + b)(a² - ab + b²)
    • Cube of binomial: (a + b)^3 = a³ + 3a²b + 3ab² + b³
    Proof Methods
    • Difference of cubes: expand using distributive property
    • Sum of cubes: factor into product of binomials
    • Both formulas can be factored into difference of cubes
    Applications
    • Formulas help factor expressions in cubic form
    • Useful for algebraic simplification and factoring
    • Common in various fields including algebra and mathematics

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