因数 49t^6-4k^8

解

因数

49 t^{6} - 4 k^{8}

(7 t^{3} + 2 k^{4}) (7 t^{3} - 2 k^{4})

解答ステップ

49 t^{6} - 4 k^{8}

49 t^{6} = (7 t^{3})^{2}

4 k^{8} = (2 k^{4})^{2}

= (7 t^{3})^{2} - (2 k^{4})^{2}

2乗の差の公式を適用する:

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

(7 t^{3})^{2} - (2 k^{4})^{2} = (7 t^{3} + 2 k^{4}) (7 t^{3} - 2 k^{4})

= (7 t^{3} + 2 k^{4}) (7 t^{3} - 2 k^{4})