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(x+5)(x+1)(x+4)

2 min read Jun 16, 2024
(x+5)(x+1)(x+4)

Expanding and Simplifying (x+5)(x+1)(x+4)

This article will guide you through expanding and simplifying the expression (x+5)(x+1)(x+4). We'll break down the steps and explain the process.

Step 1: Expand the First Two Factors

Begin by expanding the first two factors, (x+5)(x+1), using the FOIL method (First, Outer, Inner, Last):

  • First: x * x = x²
  • Outer: x * 1 = x
  • Inner: 5 * x = 5x
  • Last: 5 * 1 = 5

Combining these terms, we get: (x+5)(x+1) = x² + x + 5x + 5 = x² + 6x + 5

Step 2: Multiply the Result by the Third Factor

Now we have (x² + 6x + 5)(x+4). To expand this, we need to multiply each term in the first expression by each term in the second expression.

  • x² * x = x³
  • x² * 4 = 4x²
  • 6x * x = 6x²
  • 6x * 4 = 24x
  • 5 * x = 5x
  • 5 * 4 = 20

Step 3: Combine Like Terms

Finally, combine the like terms to simplify the expression:

x³ + 4x² + 6x² + 24x + 5x + 20 = x³ + 10x² + 29x + 20

Conclusion

Therefore, the expanded and simplified form of (x+5)(x+1)(x+4) is x³ + 10x² + 29x + 20.

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