Factoring Difference of Squares Math Example 4

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Example 4

hard
Factor x4−81x^4 - 81 completely.

Solution

  1. 1
    x4−81=(x2)2−92=(x2+9)(x2−9)x^4 - 81 = (x^2)^2 - 9^2 = (x^2 + 9)(x^2 - 9).
  2. 2
    x2−9=(x+3)(x−3)x^2 - 9 = (x+3)(x-3), so fully factored: (x2+9)(x+3)(x−3)(x^2 + 9)(x + 3)(x - 3).

Answer

(x2+9)(x+3)(x−3)(x^2 + 9)(x + 3)(x - 3)
Some expressions require multiple rounds of factoring. After the first difference of squares, check if either factor can be factored further. Note x2+9x^2 + 9 cannot be factored over the reals.

About Factoring Difference of Squares

Recognizing and factoring expressions of the form a2−b2a^2 - b^2 into the product (a+b)(a−b)(a + b)(a - b).

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More Factoring Difference of Squares Examples

Example 1 easy

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Example 2 medium

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Example 3 easy

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