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(3x+4)(2x-3)+(5x-4)(x+2)

2 min read Jun 16, 2024
(3x+4)(2x-3)+(5x-4)(x+2)

Expanding and Simplifying the Expression: (3x+4)(2x-3)+(5x-4)(x+2)

This article will guide you through the process of expanding and simplifying the given expression: (3x+4)(2x-3)+(5x-4)(x+2).

Step 1: Expanding the Expressions

We start by applying the distributive property (also known as FOIL) to each set of parentheses.

  • (3x+4)(2x-3):

    • (3x * 2x) + (3x * -3) + (4 * 2x) + (4 * -3)
    • 6x² - 9x + 8x - 12
    • 6x² - x - 12

  • (5x-4)(x+2):

    • (5x * x) + (5x * 2) + (-4 * x) + (-4 * 2)
    • 5x² + 10x - 4x - 8
    • 5x² + 6x - 8

Step 2: Combining Like Terms

Now, we combine the simplified expressions from step 1:

(6x² - x - 12) + (5x² + 6x - 8)

Combine the x² terms, the x terms, and the constant terms:

  • 6x² + 5x² = 11x²
  • -x + 6x = 5x
  • -12 - 8 = -20

Step 3: The Simplified Expression

After combining like terms, the final simplified expression is:

11x² + 5x - 20

Therefore, the expanded and simplified form of the given expression (3x+4)(2x-3)+(5x-4)(x+2) is 11x² + 5x - 20.

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