(x-5)(x+8)-(x+4)(x-1)

Jasonbradley

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Jun 17, 2024

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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
• (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

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.