因式分解 169a^4-121b^4

解答

因式分解

169 a^{4} - 121 b^{4}

(13 a^{2} + 11 b^{2}) (13 a^{2} - 11 b^{2})

求解步骤

169 a^{4} - 121 b^{4}

169 a^{4} = (13 a^{2})^{2}

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

= (13 a^{2})^{2} - (11 b^{2})^{2}

使用平方差公式:

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

(13 a^{2})^{2} - (11 b^{2})^{2} = (13 a^{2} + 11 b^{2}) (13 a^{2} - 11 b^{2})

= (13 a^{2} + 11 b^{2}) (13 a^{2} - 11 b^{2})

s im pl i f y \frac{( 9 x ^{3} - 9 x )}{( - 18 x ^{3} + 18 x )}

s im pl i f y lo g_{10} (a^{2}) b^{3} c^{5}

s im pl i f y \frac{( b ^{\frac{1}{3}} )}{( b ^{- \frac{3}{2}} \cdot b ^{\frac{1}{2}} )}

s im pl i f y \frac{4}{3} \cdot n^{5} - \frac{1}{3} \cdot n^{4} + \frac{2}{3} \cdot n^{3} - \frac{5}{3} \cdot n^{2}

s im pl i f y (2 x + 5)^{3} + (5 x - 3)^{3}