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30 April, 16:57

Which identity could be used to rewrite x^4-16

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Answers (2)
  1. 30 April, 17:27
    0
    The correct answer is,

    x⁴ - 16 = (x² + 4) (x + 2) (x - 2)

    Step-by-step explanation:

    Identity

    (x² - y²) = (x + y) (x - y)

    To rewrite x⁴ - 16

    Using identity we can write,

    x⁴ - 16 = [ (x²) ² - 4²]

    = (x² + 4) (x² - 4)

    = (x² + 4) (x - 2²)

    = (x² + 4) (x + 2) (x - 2)

    Therefore x⁴ - 16 = (x² + 4) (x + 2) (x - 2)
  2. 30 April, 19:11
    0
    - Rewrite it in the form a^2-b^2, where a=x^2 and b=4.

    - (x^2) ^2 - 4^2

    - Use difference of squares.

    - (x ^2 + 4) (x^ 2 - 4)

    - Rewrite {x}^{2}-4x 2 - 4 in the form {a}^{2}-{b}^{2}a 2 - b 2 , where a=xa=x and b=2b=2.

    - (x ^2 + 4) (x ^2 - 2^2 )

    - Use difference of squares

    - (x^2 + 4) (x+2) (x-2)

    Done.
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