(x-6)-2x%5E2%2B3x%2B30-simplified.jpeg "(2x+3)(x-6)-2x^2+3x+30 Simplified")
Simplifying the Expression (2x+3)(x-6)-2x^2+3x+30
Let's simplify the expression (2x+3)(x-6)-2x^2+3x+30 step by step.
1. Expanding the Product
First, we need to expand the product (2x+3)(x-6) using the FOIL method:
- 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
2. Combining Like Terms
Now, let's combine the like terms in the entire expression:
2x² - 12x + 3x - 18 - 2x² + 3x + 30
Combining the x² terms: 2x² - 2x² = 0
Combining the x terms: -12x + 3x + 3x = -6x
Combining the constant terms: -18 + 30 = 12
3. Simplified Expression
Finally, the simplified expression is:
0 - 6x + 12 = -6x + 12
Therefore, the simplified form of the expression (2x+3)(x-6)-2x^2+3x+30 is -6x + 12.