Jasonbradley
Home

(x-4)(x^2+4x+16)

2 min read Jun 17, 2024
(x-4)(x^2+4x+16)

Factoring the Expression: (x-4)(x^2+4x+16)

This expression represents a special case of factoring called the difference of cubes.

Understanding the Difference of Cubes

The difference of cubes formula states: a³ - b³ = (a - b)(a² + ab + b²)

Applying the Formula

  1. Identify the cubes: In our expression, x³ is the first cube (a³) and 4³ is the second cube (b³).
  2. Apply the formula: Substitute a = x and b = 4 into the difference of cubes formula: (x - 4)(x² + x * 4 + 4²)
  3. Simplify: This simplifies to (x - 4)(x² + 4x + 16)

The Result

Therefore, the factored form of (x - 4)(x² + 4x + 16) is x³ - 64.

Key Points

  • The expression (x² + 4x + 16) is a perfect square trinomial and cannot be factored further using real numbers.
  • The difference of cubes formula is a powerful tool for factoring expressions that involve cubes.
  • Recognizing the pattern of the difference of cubes allows for a quick and efficient factorization.

Related Post

Featured Posts