因数 16m^2-40mn+25n^2

解

因数

16 m^{2} - 40 mn + 25 n^{2}

(4 m - 5 n)^{2}

解答ステップ

16 m^{2} - 40 mn + 25 n^{2}

a^{2} + 2 ab + b^{2}

の形式で書き直す

:

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

25 n^{2} = (5 n)^{2}

- 40 mn = - 2 \cdot 4 m \cdot 5 n

= (4 m)^{2} - 2 \cdot 4 m \cdot 5 n + (5 n)^{2}

完全平方式を適用する:

a^{2} - 2 ab + b^{2} = (a - b)^{2}

(4 m)^{2} - 2 \cdot 4 m \cdot 5 n + (5 n)^{2} = (4 m - 5 n)^{2}

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