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(x-8)(x+4)+(x-3)(x+9)

2 min read Jun 17, 2024
(x-8)(x+4)+(x-3)(x+9)

Expanding and Simplifying the Expression: (x-8)(x+4) + (x-3)(x+9)

This article will explore how to expand and simplify the expression: (x-8)(x+4) + (x-3)(x+9).

Expanding the Products

We start by applying the FOIL method (First, Outer, Inner, Last) to each of the two products:

  • (x-8)(x+4)

    • First: x * x = x²
    • Outer: x * 4 = 4x
    • Inner: -8 * x = -8x
    • Last: -8 * 4 = -32

  • (x-3)(x+9)

    • First: x * x = x²
    • Outer: x * 9 = 9x
    • Inner: -3 * x = -3x
    • Last: -3 * 9 = -27

Combining these terms, we get:

x² + 4x - 8x - 32 + x² + 9x - 3x - 27

Simplifying the Expression

Now, we combine like terms:

  • x² + x² = 2x²
  • 4x - 8x + 9x - 3x = 2x
  • -32 - 27 = -59

Therefore, the simplified expression is: 2x² + 2x - 59

Conclusion

By applying the FOIL method and combining like terms, we have successfully expanded and simplified the expression (x-8)(x+4) + (x-3)(x+9) to 2x² + 2x - 59. This process demonstrates how algebraic manipulation can be used to express complex expressions in a more concise and understandable form.

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