(x%2B4)-(2x%2B5)(3x-4).jpeg "(5x-3)(x+4)-(2x+5)(3x-4)")
Expanding and Simplifying the Expression: (5x-3)(x+4)-(2x+5)(3x-4)
This article will guide you through the process of expanding and simplifying the given algebraic expression: (5x-3)(x+4)-(2x+5)(3x-4).
Expanding the Products
First, we need to expand each of the products using the distributive property (also known as FOIL method).
- (5x-3)(x+4):
- 5x * x + 5x * 4 - 3 * x - 3 * 4 = 5x² + 20x - 3x - 12
- (2x+5)(3x-4):
- 2x * 3x + 2x * -4 + 5 * 3x + 5 * -4 = 6x² - 8x + 15x - 20
Now our expression looks like this: 5x² + 20x - 3x - 12 - (6x² - 8x + 15x - 20)
Combining Like Terms
Next, we simplify each part of the expression by combining like terms.
- 5x² + 20x - 3x - 12:
- 5x² + (20x - 3x) - 12 = 5x² + 17x - 12
- 6x² - 8x + 15x - 20:
- 6x² + (-8x + 15x) - 20 = 6x² + 7x - 20
Our expression now becomes: 5x² + 17x - 12 - (6x² + 7x - 20)
Distributing the Negative Sign
Remember that the minus sign before the parentheses means we need to multiply each term inside the parentheses by -1.
- -(6x² + 7x - 20):
- -1 * 6x² + (-1) * 7x + (-1) * -20 = -6x² - 7x + 20
Now our expression is: 5x² + 17x - 12 - 6x² - 7x + 20
Final Simplification
Finally, we combine like terms again to arrive at the simplified expression.
- 5x² + 17x - 12 - 6x² - 7x + 20:
- (5x² - 6x²) + (17x - 7x) + (-12 + 20) = -x² + 10x + 8
Therefore, the simplified form of the expression (5x-3)(x+4)-(2x+5)(3x-4) is -x² + 10x + 8.