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Factor the expression: x^6-729. Show your work Please.
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Factor the expression: x^6-729. Show your work Please.

User Greg Dan
by
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1 Answer

1 vote

Answer:

  • (x + 3)(x - 3)(x^2 -3x + 9)(x^2 + 3x + 9)

Explanation:

Use of formulas:

  • a^2 - b^2 = (a + b)(a -b)
  • a^3 + b^3 = (a + b)(a^2 - ab + b^2)
  • a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Given the expression:

  • x^6-729

Factoring 729

  • 729 = 3*3*3*3*3*3 = 3^6

Factoring the expression

  • x^6 - 3^6 =
  • (x^3)^2 - (3^3)^2 =
  • (x^3 + 3^3)(x^3 - 3^3) =
  • (x + 3)(x^2 -3x + 9)(x - 3)(x^2 + 3x + 9) =
  • (x + 3)(x - 3)(x^2 -3x + 9)(x^2 + 3x + 9)
User Athina
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