(2x%2B3)-2x(x-3)%2Bx%2B7.jpeg "(x-5)(2x+3)-2x(x-3)+x+7")
Simplifying the Expression (x-5)(2x+3)-2x(x-3)+x+7
This article will walk you through the process of simplifying the expression (x-5)(2x+3)-2x(x-3)+x+7.
Expanding the Expression
First, we need to expand the expression by applying the distributive property.
- (x-5)(2x+3):
- Multiply each term in the first set of parentheses by each term in the second set:
- x * 2x = 2x²
- x * 3 = 3x
- -5 * 2x = -10x
- -5 * 3 = -15
- Combine the terms: 2x² + 3x - 10x - 15 = 2x² - 7x - 15
- Multiply each term in the first set of parentheses by each term in the second set:
- -2x(x-3):
- Multiply -2x by each term in the parentheses:
- -2x * x = -2x²
- -2x * -3 = 6x
- Combine the terms: -2x² + 6x
- Multiply -2x by each term in the parentheses:
Now our expression looks like this: 2x² - 7x - 15 - 2x² + 6x + x + 7
Combining Like Terms
Next, we combine like terms:
- 2x² - 2x² = 0
- -7x + 6x + x = 0
- -15 + 7 = -8
The Simplified Expression
Finally, we have our simplified expression: -8
Therefore, the simplified form of the expression (x-5)(2x+3)-2x(x-3)+x+7 is -8.