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Mariana [72]
3 years ago
9

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

Mathematics
1 answer:
Brut [27]3 years ago
7 0

Answer:

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

Step-by-step explanation:

<u><em>Use of formulas:</em></u>

  • <em>a^2 - b^2 = (a + b)(a -b)</em>
  • <em>a^3 + b^3 = (a + b)(a^2 - ab + b^2)</em>
  • <em>a^3 - b^3 = (a - b)(a^2 + ab + b^2)</em>

<u>Given the expression: </u>

  • x^6-729

<u>Factoring 729</u>

  • 729 = 3*3*3*3*3*3 = 3^6

<u>Factoring the expression </u>

  • 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)
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