因式分解 9m^4+14m^2*n^2+25n^4

解答

因式分解

9 m^{4} + 14 m^{2} \cdot n^{2} + 25 n^{4}

(3 m^{2} + 5 n^{2} + 4 mn) (3 m^{2} + 5 n^{2} - 4 mn)

求解步骤

9 m^{4} + 14 m^{2} n^{2} + 25 n^{4}

加和减

16 m^{2} n^{2}

= 9 m^{4} + 30 m^{2} n^{2} + 25 n^{4} - 16 m^{2} n^{2}

因式分解

9 m^{4} + 30 m^{2} n^{2} + 25 n^{4} : (3 m^{2} + 5 n^{2})^{2}

= (3 m^{2} + 5 n^{2})^{2} - 16 m^{2} n^{2}

使用指数运算法则

= (3 m^{2} + 5 n^{2})^{2} - (4 mn)^{2}

因式分解

(3 m^{2} + 5 n^{2})^{2} - (4 mn)^{2} : (3 m^{2} + 5 n^{2} + 4 mn) (3 m^{2} + 5 n^{2} - 4 mn)

= (3 m^{2} + 5 n^{2} + 4 mn) (3 m^{2} + 5 n^{2} - 4 mn)

s im pl i f y - sin^{2} (x) - cos^{2} (x) + sin (x)

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

s im pl i f y \frac{( 2 ^{n + 1} + 2 ^{n} )}{( 2 ^{n + 4} - 2 ^{n + 1} )}

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

f a c t or x^{29} - x^{24} + x^{13} - 1