簡約 (8m^9n^2-10m^7n^4-20m^5n^6+12m^3n^8)/(2m^2)

解

簡約

\frac{8 m ^{9} n ^{2} - 10 m ^{7} n ^{4} - 20 m ^{5} n ^{6} + 12 m ^{3} n ^{8}}{2 m ^{2}}

m n^{2} (4 m^{6} - 5 m^{4} n^{2} - 10 m^{2} n^{4} + 6 n^{6})

解答ステップ

\frac{8 m ^{9} n ^{2} - 10 m ^{7} n ^{4} - 20 m ^{5} n ^{6} + 12 m ^{3} n ^{8}}{2 m ^{2}}

因数

8 m^{9} n^{2} - 10 m^{7} n^{4} - 20 m^{5} n^{6} + 12 m^{3} n^{8} : 2 m^{3} n^{2} (4 m^{6} - 5 m^{4} n^{2} - 10 m^{2} n^{4} + 6 n^{6})

= \frac{2 m ^{3} n ^{2} ( 4 m ^{6} - 5 m ^{4} n ^{2} - 10 m ^{2} n ^{4} + 6 n ^{6} )}{2 m ^{2}}

共通因数を約分する:

2

= \frac{m ^{3} n ^{2} ( 4 m ^{6} - 5 m ^{4} n ^{2} - 10 m ^{2} n ^{4} + 6 n ^{6} )}{m ^{2}}

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

m^{3} = m^{2} m

= \frac{m ^{2} m n ^{2} ( 4 m ^{6} - 5 m ^{4} n ^{2} - 10 m ^{2} n ^{4} + 6 n ^{6} )}{m ^{2}}

共通因数を約分する:

m^{2}

= m n^{2} (4 m^{6} - 5 m^{4} n^{2} - 10 m^{2} n^{4} + 6 n^{6})