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(3x+2)^2+(2x-7)^2-2(3x+2)(2x+5)

2 min read Jun 16, 2024
(3x+2)^2+(2x-7)^2-2(3x+2)(2x+5)

Simplifying the Expression (3x + 2)² + (2x - 7)² - 2(3x + 2)(2x + 5)

This expression involves expanding squares and then combining like terms. Let's break down the steps:

1. Expanding the Squares

  • (3x + 2)²: This is a perfect square trinomial. We can use the formula (a + b)² = a² + 2ab + b²
    • (3x + 2)² = (3x)² + 2(3x)(2) + 2² = 9x² + 12x + 4
  • (2x - 7)²: Again, we use the formula (a - b)² = a² - 2ab + b²
    • (2x - 7)² = (2x)² - 2(2x)(7) + 7² = 4x² - 28x + 49

2. Expanding the Product

  • -2(3x + 2)(2x + 5): We can use the FOIL method (First, Outer, Inner, Last) to expand this.
    • -2[(3x)(2x) + (3x)(5) + (2)(2x) + (2)(5)] = -2(6x² + 15x + 4x + 10) = -12x² - 38x - 20

3. Combining Like Terms

Now we have: (9x² + 12x + 4) + (4x² - 28x + 49) - (12x² - 38x - 20)

Combining the x² terms: 9x² + 4x² - 12x² = x²

Combining the x terms: 12x - 28x + 38x = 22x

Combining the constant terms: 4 + 49 + 20 = 73

Final Result

Therefore, the simplified expression is: x² + 22x + 73

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