(x%2B8)-(x%2B4)(x-1).jpeg "(x-5)(x+8)-(x+4)(x-1)")
Expanding and Simplifying the Expression (x-5)(x+8)-(x+4)(x-1)
This article will guide you through the process of expanding and simplifying the algebraic expression (x-5)(x+8)-(x+4)(x-1). We will use the distributive property (also known as FOIL) to expand the products and then combine like terms to reach a simplified form.
Expanding the Products
- (x-5)(x+8):
- Using FOIL, we multiply each term in the first set of parentheses by each term in the second set:
- x * x = x²
- x * 8 = 8x
- -5 * x = -5x
- -5 * 8 = -40
- Combining these terms, we get: x² + 8x - 5x - 40
- Using FOIL, we multiply each term in the first set of parentheses by each term in the second set:
- (x+4)(x-1):
- Applying FOIL again:
- x * x = x²
- x * -1 = -x
- 4 * x = 4x
- 4 * -1 = -4
- Combining the terms gives us: x² - x + 4x - 4
- Applying FOIL again:
Combining Like Terms
Now, let's substitute these expanded products back into the original expression:
(x-5)(x+8)-(x+4)(x-1) = (x² + 8x - 5x - 40) - (x² - x + 4x - 4)
Next, we distribute the negative sign in front of the second set of parentheses:
= x² + 8x - 5x - 40 - x² + x - 4x + 4
Finally, we combine like terms:
= (x² - x²) + (8x - 5x + x - 4x) + (-40 + 4)
= 0x + 0x - 36
= -36
Conclusion
Therefore, the simplified form of the expression (x-5)(x+8)-(x+4)(x-1) is -36. This means that regardless of the value of 'x', the expression will always evaluate to -36.