(2x+5)(x-2)-3(x+2)^2+(x+1)^2

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (2x+5)(x-2)-3(x+2)^2+(x+1)^2

This article aims to simplify the given algebraic expression: (2x+5)(x-2)-3(x+2)^2+(x+1)^2.

To simplify this expression, we need to follow the order of operations (PEMDAS/BODMAS) and use the distributive property, as well as the rules for squaring binomials.

Step 1: Expand the Products

• (2x+5)(x-2): Using the FOIL method (First, Outer, Inner, Last), we get:

  • 2x * x = 2x²
  • 2x * -2 = -4x
  • 5 * x = 5x
  • 5 * -2 = -10
  • Combining like terms: 2x² + x - 10

• -3(x+2)²: Squaring a binomial: (a+b)² = a² + 2ab + b²

  • -3 (x² + 4x + 4) = -3x² - 12x - 12

• (x+1)²: Squaring a binomial: (a+b)² = a² + 2ab + b²

  • x² + 2x + 1

Step 2: Combine Like Terms

Now we have: 2x² + x - 10 - 3x² - 12x - 12 + x² + 2x + 1

Combining like terms:

• x² terms: 2x² - 3x² + x² = 0
• x terms: x - 12x + 2x = -9x
• Constant terms: -10 - 12 + 1 = -21

Final Simplified Expression

Therefore, the simplified expression is: -9x - 21