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(x+8)(x-5)+(x-4)(x-6)

2 min read Jun 17, 2024
(x+8)(x-5)+(x-4)(x-6)

Simplifying the Expression (x+8)(x-5)+(x-4)(x-6)

This article will guide you through the process of simplifying the algebraic expression (x+8)(x-5)+(x-4)(x-6).

Expanding the Products

The expression involves two products of binomials. We can use the FOIL method (First, Outer, Inner, Last) to expand each product:

  • (x+8)(x-5):

    • First: x * x = x²
    • Outer: x * -5 = -5x
    • Inner: 8 * x = 8x
    • Last: 8 * -5 = -40
    • Combined: x² - 5x + 8x - 40 = x² + 3x - 40

  • (x-4)(x-6):

    • First: x * x = x²
    • Outer: x * -6 = -6x
    • Inner: -4 * x = -4x
    • Last: -4 * -6 = 24
    • Combined: x² - 6x - 4x + 24 = x² - 10x + 24

Combining Like Terms

Now, our expression becomes: (x² + 3x - 40) + (x² - 10x + 24)

Combine the like terms:

  • x² + x² = 2x²
  • 3x - 10x = -7x
  • -40 + 24 = -16

Simplified Expression

The simplified form of the expression is: 2x² - 7x - 16

Therefore, (x+8)(x-5)+(x-4)(x-6) = 2x² - 7x - 16.

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