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(x+3)(x+4)(x+5)

2 min read Jun 16, 2024
(x+3)(x+4)(x+5)

Expanding the Expression (x+3)(x+4)(x+5)

This article will guide you through the process of expanding the expression (x+3)(x+4)(x+5).

Step 1: Expand the first two factors

Begin by expanding the first two factors, (x+3)(x+4), using the FOIL method (First, Outer, Inner, Last):

  • First: x * x = x²
  • Outer: x * 4 = 4x
  • Inner: 3 * x = 3x
  • Last: 3 * 4 = 12

Combine the terms: (x+3)(x+4) = x² + 4x + 3x + 12 = x² + 7x + 12

Step 2: Multiply the result by the remaining factor

Now we have (x² + 7x + 12)(x+5). We need to multiply each term in the first trinomial by each term in the second binomial:

  • x² * x = x³
  • x² * 5 = 5x²
  • 7x * x = 7x²
  • 7x * 5 = 35x
  • 12 * x = 12x
  • 12 * 5 = 60

Step 3: Combine like terms

Combine all the terms with the same power of x:

x³ + 5x² + 7x² + 35x + 12x + 60 = x³ + 12x² + 47x + 60

Conclusion

Therefore, the expanded form of (x+3)(x+4)(x+5) is x³ + 12x² + 47x + 60.

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