(x-4)-(x%2B2)(x-7).jpeg "(x+5)(x-4)-(x+2)(x-7)")
Simplifying the Expression: (x+5)(x-4) - (x+2)(x-7)
This article will guide you through the process of simplifying the expression (x+5)(x-4) - (x+2)(x-7).
Expanding the Products
The expression involves two products of binomials. We can expand these products using the FOIL method (First, Outer, Inner, Last):
- (x+5)(x-4):
- First: x * x = x²
- Outer: x * -4 = -4x
- Inner: 5 * x = 5x
- Last: 5 * -4 = -20
Combining these terms, we get: x² - 4x + 5x - 20
- (x+2)(x-7):
- First: x * x = x²
- Outer: x * -7 = -7x
- Inner: 2 * x = 2x
- Last: 2 * -7 = -14
Combining these terms, we get: x² - 7x + 2x - 14
Combining the Expanded Terms
Now, we can substitute the expanded forms back into the original expression:
(x² - 4x + 5x - 20) - (x² - 7x + 2x - 14)
Next, we can distribute the negative sign:
x² - 4x + 5x - 20 - x² + 7x - 2x + 14
Simplifying by Combining Like Terms
Finally, we combine the like terms:
- x² - x² = 0
- -4x + 5x + 7x - 2x = 6x
- -20 + 14 = -6
Therefore, the simplified form of the expression is 6x - 6.
Conclusion
By expanding the products and combining like terms, we successfully simplified the expression (x+5)(x-4) - (x+2)(x-7) to 6x - 6. This process demonstrates the importance of using algebraic techniques to manipulate and simplify expressions.