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(x+6)(x+3)(x−5)

2 min read Jun 17, 2024
(x+6)(x+3)(x−5)

Expanding and Simplifying (x+6)(x+3)(x-5)

This article will guide you through the process of expanding and simplifying the expression (x+6)(x+3)(x-5).

Step 1: Expand the First Two Factors

Begin by expanding the first two factors, (x+6)(x+3), using the FOIL method (First, Outer, Inner, Last):

  • First: x * x = x²
  • Outer: x * 3 = 3x
  • Inner: 6 * x = 6x
  • Last: 6 * 3 = 18

Combining these terms, we get: (x+6)(x+3) = x² + 3x + 6x + 18 = x² + 9x + 18

Step 2: Multiply the Result by (x-5)

Now, multiply the simplified expression (x² + 9x + 18) by (x-5) using the distributive property:

  • x² * (x-5) = x³ - 5x²
  • 9x * (x-5) = 9x² - 45x
  • 18 * (x-5) = 18x - 90

Step 3: Combine Like Terms

Finally, combine the like terms to obtain the fully expanded and simplified expression:

x³ - 5x² + 9x² - 45x + 18x - 90 = x³ + 4x² - 27x - 90

Conclusion

Therefore, the expanded and simplified form of (x+6)(x+3)(x-5) is x³ + 4x² - 27x - 90.

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