因式分解 16m^2-81n^2

解答

因式分解

16 m^{2} - 81 n^{2}

(4 m + 9 n) (4 m - 9 n)

求解步骤

16 m^{2} - 81 n^{2}

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

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

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

使用平方差公式:

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

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

= (4 m + 9 n) (4 m - 9 n)

e x p an d (3 m - 2 n^{2})^{3}

s im pl i f y 2 cos (x) \cdot sin (x)

s im pl i f y (\frac{1 + i}{1 - i})^{8}

e x p an d (a^{3} + b^{3})^{2}

\frac{46}{7}