(3x%5E2-2x%2B1).jpeg "(4x-3)(3x^2-2x+1)")
Expanding the Expression (4x - 3)(3x² - 2x + 1)
This article will guide you through the process of expanding the expression (4x - 3)(3x² - 2x + 1).
Understanding the Process
Expanding this expression means multiplying each term in the first set of parentheses with each term in the second set of parentheses. This is a common technique used in algebra, often referred to as FOIL (First, Outer, Inner, Last) when dealing with binomials. However, in this case, we have a binomial multiplied by a trinomial.
Step-by-Step Expansion
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Multiply the first term of the first set with each term in the second set: (4x)(3x²) = 12x³ (4x)(-2x) = -8x² (4x)(1) = 4x
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Multiply the second term of the first set with each term in the second set: (-3)(3x²) = -9x² (-3)(-2x) = 6x (-3)(1) = -3
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Combine the resulting terms: 12x³ - 8x² + 4x - 9x² + 6x - 3
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Simplify by combining like terms: 12x³ - 17x² + 10x - 3
Final Result
Therefore, the expanded form of (4x - 3)(3x² - 2x + 1) is 12x³ - 17x² + 10x - 3.
Additional Notes
- The expansion process involves applying the distributive property of multiplication.
- The final result is a polynomial with a degree of 3 (cubic polynomial).
- Expanding expressions is an essential step in simplifying and solving algebraic equations.