factor-x^{16}z^{16}+y^{16}

الحلّ

factor

- x^{16} z^{16} + y^{16}

(y^{8} + x^{8} z^{8}) (y^{4} + x^{4} z^{4}) (y^{2} + x^{2} z^{2}) (y + x z) (y - x z)

خطوات الحلّ

- x^{16} z^{16} + y^{16}

(x z)^{16}

كـ

x^{16} z^{16}

اكتب مجددًا

= - (x z)^{16} + y^{16}

(y^{8})^{2} - ((x z)^{8})^{2}

كـ

y^{16} - (x z)^{16}

اكتب مجددًا

= (y^{8})^{2} - ((x z)^{8})^{2}

x^{2} - y^{2} = (x + y) (x - y)

فعّل قانون فرق المربّعات

(y^{8})^{2} - ((x z)^{8})^{2} = (y^{8} + (x z)^{8}) (y^{8} - (x z)^{8})

= (y^{8} + (x z)^{8}) (y^{8} - (x z)^{8})

y^{8} - (x z)^{8}

حلل إلى عوامل:

(y^{4} + (x z)^{4}) (y^{2} + (x z)^{2}) (y + x z) (y - x z)

= (y^{8} + (x z)^{8}) (y^{4} + (x z)^{4}) (y^{2} + (x z)^{2}) (y + x z) (y - x z)

(y^{8} + (x z)^{8}) (y^{4} + (x z)^{4}) (y^{2} + (x z)^{2}) (y + x z) (y - x z)

بسّط:

(y^{8} + x^{8} z^{8}) (y^{4} + x^{4} z^{4}) (y^{2} + x^{2} z^{2}) (y + x z) (y - x z)

= (y^{8} + x^{8} z^{8}) (y^{4} + x^{4} z^{4}) (y^{2} + x^{2} z^{2}) (y + x z) (y - x z)

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