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(x-2)(6-4x)+(5x+4)(x-2)

2 min read Jun 17, 2024
(x-2)(6-4x)+(5x+4)(x-2)

Factoring and Simplifying Algebraic Expressions: (x-2)(6-4x)+(5x+4)(x-2)

This article will guide you through the process of factoring and simplifying the algebraic expression: (x-2)(6-4x)+(5x+4)(x-2).

Understanding the Expression

The expression consists of two terms, both of which are products of binomials:

  • (x-2)(6-4x)
  • (5x+4)(x-2)

Notice that both terms share a common factor: (x-2).

Simplifying using Distributive Property and Factoring

  1. Identify the common factor: (x-2) is common to both terms.

  2. Factor out the common factor: (x-2)(6-4x) + (5x+4)(x-2) = (x-2)[(6-4x) + (5x+4)]

  3. Simplify the expression inside the brackets: (x-2)[(6-4x) + (5x+4)] = (x-2)(x+10)

  4. Expand the final expression (optional): (x-2)(x+10) = x² + 8x - 20

Final Result

The simplified form of the expression is (x-2)(x+10) or, if expanded, x² + 8x - 20.

Key Takeaways

  • Recognizing common factors is crucial for simplifying complex expressions.
  • The distributive property helps us factor out common terms.
  • Factoring and simplifying expressions can make them easier to work with in further calculations.

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