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Factor the following completely
x^4 – 625

  • Math -

    call y = x^2 so x = +/- sqrt y
    then
    y^2 = 625
    y = 25 or y = -25
    x = sqrt 25 = +5 or -5
    y = sqrt-25 = +5i or -5i

  • Math -

    Any expression of the form a^2 - b^2 can be written as (a + b)(a - b).

    Therefore, x^4 - 625) = (x^2 + 25)(x^2 - 25).

    Then, (x^2 + 25)(x + 5)(x - 5)

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