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(4x-5)(2x+3)-4(x+2)(2x-1)+(10x+7)

2 min read Jun 16, 2024
(4x-5)(2x+3)-4(x+2)(2x-1)+(10x+7)

Simplifying the Expression: (4x-5)(2x+3)-4(x+2)(2x-1)+(10x+7)

This article will guide you through the process of simplifying the given algebraic expression: (4x-5)(2x+3)-4(x+2)(2x-1)+(10x+7). We will use the distributive property and combine like terms to reach a simplified form.

Step 1: Expanding the Products

First, we expand the products using the distributive property (also known as FOIL - First, Outer, Inner, Last):

  • (4x-5)(2x+3) = (4x * 2x) + (4x * 3) + (-5 * 2x) + (-5 * 3) = 8x² + 12x - 10x - 15
  • 4(x+2)(2x-1) = 4 * [(x * 2x) + (x * -1) + (2 * 2x) + (2 * -1)] = 4 * (2x² - x + 4x - 2) = 8x² - 4x + 16x - 8

Step 2: Combining Terms

Now, let's substitute the expanded products back into the original expression:

(8x² + 12x - 10x - 15) - (8x² - 4x + 16x - 8) + (10x + 7)

Next, we combine like terms:

  • x² terms: 8x² - 8x² = 0
  • x terms: 12x - 10x + 4x - 16x + 10x = 10x
  • Constant terms: -15 + 8 + 7 = 0

Step 3: Final Simplified Form

After combining all the terms, the simplified form of the expression is:

10x

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