因式分解 49x^2y^6z^{10}-a^{12}

解答

因式分解

49 x^{2} \cdot y^{6} \cdot z^{10} - a^{12}

(7 x y^{3} z^{5} + a^{6}) (7 x y^{3} z^{5} - a^{6})

求解步骤

49 x^{2} y^{6} z^{10} - a^{12}

49 x^{2} y^{6} z^{10} = (7 x y^{3} z^{5})^{2}

a^{12} = (a^{6})^{2}

= (7 x y^{3} z^{5})^{2} - (a^{6})^{2}

使用平方差公式:

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

(7 x y^{3} z^{5})^{2} - (a^{6})^{2} = (7 x y^{3} z^{5} + a^{6}) (7 x y^{3} z^{5} - a^{6})

= (7 x y^{3} z^{5} + a^{6}) (7 x y^{3} z^{5} - a^{6})

f a c t or a^{4} - b^{4} + 2 b^{2} - 1

s im pl i f y \frac{( x ^{2} + 1 - 7 x ) - ( x + 2 )}{x - 1}

e x p an d (x - y)^{2} - 9

s im pl i f y \frac{2 sin ( x ) - 4 sin ( x ) - cos ( x )}{2}

s im pl i f y (8 x^{2} + 7 x + 10) + (- 2 x^{3} + 7 x + 4)