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(x+7)(x-2)-(x+9)(x-4)

2 min read Jun 17, 2024
(x+7)(x-2)-(x+9)(x-4)

Simplifying the Expression (x+7)(x-2)-(x+9)(x-4)

This article will guide you through simplifying the expression (x+7)(x-2)-(x+9)(x-4). We'll break down each step to understand the process clearly.

Expanding the Expressions

The first step is to expand the two products using the FOIL (First, Outer, Inner, Last) method.

  • (x+7)(x-2):

    • First: x * x = x²
    • Outer: x * -2 = -2x
    • Inner: 7 * x = 7x
    • Last: 7 * -2 = -14
    • Combined: x² -2x + 7x - 14 = x² + 5x - 14

  • (x+9)(x-4):

    • First: x * x = x²
    • Outer: x * -4 = -4x
    • Inner: 9 * x = 9x
    • Last: 9 * -4 = -36
    • Combined: x² - 4x + 9x - 36 = x² + 5x - 36

Combining Like Terms

Now, we can substitute the expanded expressions back into the original equation:

(x² + 5x - 14) - (x² + 5x - 36)

Remember that subtracting a whole expression means changing the sign of each term within it:

x² + 5x - 14 - x² - 5x + 36

Finally, we combine like terms:

  • x² - x² = 0
  • 5x - 5x = 0
  • -14 + 36 = 22

Final Result

The simplified expression is 22.

Therefore, (x+7)(x-2)-(x+9)(x-4) = 22.

This example showcases how using the FOIL method and combining like terms can simplify complex expressions. It's important to remember the sign rules when dealing with parentheses and subtraction.

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