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(3-2x)(2x+3) 1-2x(x+3)

less than a minute read Jun 16, 2024
(3-2x)(2x+3) 1-2x(x+3)

Simplifying the Expression: (3-2x)(2x+3) - 2x(x+3)

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

Step 1: Expand the Products

We begin by expanding the products using the distributive property (also known as FOIL method).

  • (3-2x)(2x+3):

    • 3 * 2x = 6x
    • 3 * 3 = 9
    • -2x * 2x = -4x²
    • -2x * 3 = -6x

  • 2x(x+3):

    • 2x * x = 2x²
    • 2x * 3 = 6x

This gives us: 6x + 9 - 4x² - 6x - 2x² - 6x

Step 2: Combine Like Terms

Now, we combine the terms with the same variable and exponent.

  • x² terms: -4x² - 2x² = -6x²
  • x terms: 6x - 6x - 6x = -6x
  • Constant term: +9

This simplifies our expression to: -6x² - 6x + 9

Final Result

Therefore, the simplified form of the expression (3-2x)(2x+3) - 2x(x+3) is -6x² - 6x + 9.

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