(x%2B6)-(2x-5)(x%2B10).jpeg "(2x+3)(x+6)-(2x-5)(x+10)")
Simplifying the Expression (2x+3)(x+6)-(2x-5)(x+10)
This article will guide you through simplifying the given algebraic expression: (2x+3)(x+6)-(2x-5)(x+10)
Expanding the Expressions
We will start by expanding the products using the FOIL method (First, Outer, Inner, Last).
Step 1: Expand (2x+3)(x+6)
- First: (2x)(x) = 2x²
- Outer: (2x)(6) = 12x
- Inner: (3)(x) = 3x
- Last: (3)(6) = 18
Therefore, (2x+3)(x+6) = 2x² + 12x + 3x + 18 = 2x² + 15x + 18
Step 2: Expand (2x-5)(x+10)
- First: (2x)(x) = 2x²
- Outer: (2x)(10) = 20x
- Inner: (-5)(x) = -5x
- Last: (-5)(10) = -50
Therefore, (2x-5)(x+10) = 2x² + 20x - 5x - 50 = 2x² + 15x - 50
Combining the Expanded Expressions
Now we have:
(2x² + 15x + 18) - (2x² + 15x - 50)
Step 3: Distribute the negative sign:
2x² + 15x + 18 - 2x² - 15x + 50
Step 4: Combine like terms:
(2x² - 2x²) + (15x - 15x) + (18 + 50) = 68
Conclusion
Therefore, the simplified form of the expression (2x+3)(x+6)-(2x-5)(x+10) is 68.