因式分解 121x^4-81y^6z^4

解答

因式分解

121 x^{4} - 81 y^{6} z^{4}

(11 x^{2} + 9 y^{3} z^{2}) (11 x^{2} - 9 y^{3} z^{2})

求解步骤

121 x^{4} - 81 y^{6} z^{4}

121 x^{4} = (11 x^{2})^{2}

81 y^{6} z^{4} = (9 y^{3} z^{2})^{2}

= (11 x^{2})^{2} - (9 y^{3} z^{2})^{2}

使用平方差公式:

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

(11 x^{2})^{2} - (9 y^{3} z^{2})^{2} = (11 x^{2} + 9 y^{3} z^{2}) (11 x^{2} - 9 y^{3} z^{2})

= (11 x^{2} + 9 y^{3} z^{2}) (11 x^{2} - 9 y^{3} z^{2})

f a c t or x^{3} - 2 x^{2} + 2 x - 4

s im pl i f y \frac{1}{( 1 + a ^{n - 1} )} + \frac{1}{( 1 + a ^{m - 1} )}

s im pl i f y - (x - 9)

s im pl i f y \frac{- 4 x}{2 x}

e x p an d (2 y - 5) \cdot (3 y^{3.4})