化简+(16m^4-81n^4)/(2m-3n)

解答

化简

+ \frac{16 m ^{4} - 81 n ^{4}}{2 m - 3 n}

(4 m^{2} + 9 n^{2}) (2 m + 3 n)

求解步骤

\frac{16 m ^{4} - 81 n ^{4}}{2 m - 3 n}

16 m^{4} = (4 m^{2})^{2}

81 n^{4} = (9 n^{2})^{2}

= \frac{( 4 m ^{2} ) ^{2} - ( 9 n ^{2} ) ^{2}}{2 m - 3 n}

使用平方差公式:

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

(4 m^{2})^{2} - (9 n^{2})^{2} = (4 m^{2} + 9 n^{2}) (4 m^{2} - 9 n^{2})

= \frac{( 4 m ^{2} + 9 n ^{2} ) ( 4 m ^{2} - 9 n ^{2} )}{2 m - 3 n}

因式分解

4 m^{2} - 9 n^{2} : (2 m + 3 n) (2 m - 3 n)

= \frac{( 4 m ^{2} + 9 n ^{2} ) ( 2 m + 3 n ) ( 2 m - 3 n )}{2 m - 3 n}

约分:

2 m - 3 n

= (4 m^{2} + 9 n^{2}) (2 m + 3 n)

e x p an d (x - 2 y) (x + y)

s im pl i f y 6 - \frac{1}{9}

s im pl i f y - 4 y - 2 y

f a c t or - 2 x^{3} + 26 x^{2} + 60 x

s im pl i f y 3 0^{2} + 3 0^{2}