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algebra · worked example

Solve x² - 16 = (x - 4)(x + 4)

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Problem

x2−16x^2 - 16

Step-by-step solution

  1. 將 x2−16x^2 - 16 視為 a2−b2a^2 - b^2，其中 a=xa = x、b=4b = 4（因為 42=164^2 = 16）。

  2. 套用恆等式 a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b)。

  3. 結果：(x−4)(x+4)(x - 4)(x + 4)。

Answer

(x−4)(x+4)(x - 4)(x + 4)

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