因数 49x^2-140xy+100y^2

解

因数

49 x^{2} - 140 x y + 100 y^{2}

(7 x - 10 y)^{2}

解答ステップ

49 x^{2} - 140 x y + 100 y^{2}

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

の形式で書き直す

:

49 x^{2} = (7 x)^{2}

100 y^{2} = (10 y)^{2}

- 140 x y = - 2 \cdot 7 x \cdot 10 y

= (7 x)^{2} - 2 \cdot 7 x \cdot 10 y + (10 y)^{2}

完全平方式を適用する:

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

(7 x)^{2} - 2 \cdot 7 x \cdot 10 y + (10 y)^{2} = (7 x - 10 y)^{2}

= (7 x - 10 y)^{2}