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(2x-1)(3x+2)-6x(x-1)-7x+4

2 min read Jun 16, 2024
(2x-1)(3x+2)-6x(x-1)-7x+4

Simplifying the Expression: (2x-1)(3x+2)-6x(x-1)-7x+4

This article will guide you through the process of simplifying the algebraic expression: (2x-1)(3x+2)-6x(x-1)-7x+4.

Expanding the Expression

  1. Expanding the first product:

    • We use the FOIL method to expand (2x-1)(3x+2):
      • First: (2x)(3x) = 6x²
      • Outer: (2x)(2) = 4x
      • Inner: (-1)(3x) = -3x
      • Last: (-1)(2) = -2
    • The expanded form becomes: 6x² + 4x - 3x - 2

  2. Expanding the second product:

    • We distribute the -6x to the terms inside the parentheses:
      • -6x(x-1) = -6x² + 6x

  3. Combining all terms:

    • Our expression now becomes: 6x² + 4x - 3x - 2 - 6x² + 6x - 7x + 4

Simplifying the Expression

  1. Combining like terms:

    • x² terms: 6x² - 6x² = 0
    • x terms: 4x - 3x + 6x - 7x = 0
    • Constant terms: -2 + 4 = 2

  2. Final simplified expression:

    • The simplified form of the expression is 2.

Conclusion

By carefully applying the distributive property and combining like terms, we have successfully simplified the algebraic expression (2x-1)(3x+2)-6x(x-1)-7x+4 to the constant value 2. This process demonstrates the importance of following the order of operations and utilizing algebraic techniques for simplifying complex expressions.

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