因数+16x^2-40xy+25y^2

解

因数

+ 16 x^{2} - 40 x y + 25 y^{2}

(4 x - 5 y)^{2}

解答ステップ

16 x^{2} - 40 x y + 25 y^{2}

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

の形式で書き直す

:

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

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

- 40 x y = - 2 \cdot 4 x \cdot 5 y

= (4 x)^{2} - 2 \cdot 4 x \cdot 5 y + (5 y)^{2}

完全平方式を適用する:

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

(4 x)^{2} - 2 \cdot 4 x \cdot 5 y + (5 y)^{2} = (4 x - 5 y)^{2}

= (4 x - 5 y)^{2}