Question

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

Answer 1

• (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)