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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