因数 (7z^3-xy)^4-9

解

因数

(7 z^{3} - x y)^{4} - 9

(49 z^{6} - 14 z^{3} x y + x^{2} y^{2} + 3) (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} - 3)

解答ステップ

(7 z^{3} - x y)^{4} - 9

(7 z^{3} - x y)^{4} = ((7 z^{3} - x y)^{2})^{2}

9 = 3^{2}

= ((7 z^{3} - x y)^{2})^{2} - 3^{2}

2乗の差の公式を適用する:

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

((7 z^{3} - x y)^{2})^{2} - 3^{2} = ((7 z^{3} - x y)^{2} + 3) ((7 z^{3} - x y)^{2} - 3)

= ((7 z^{3} - x y)^{2} + 3) ((7 z^{3} - x y)^{2} - 3)

簡素化

((7 z^{3} - x y)^{2} + 3) ((7 z^{3} - x y)^{2} - 3) : (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} + 3) (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} - 3)

= (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} + 3) (49 z^{6} - 14 z^{3} x y + x^{2} y^{2} - 3)