因数 (2x-k)^2-2(2x-k)(x+t)+(x+t)^2

解

因数

(2 x - k)^{2} - 2 (2 x - k) (x + t) + (x + t)^{2}

x^{2} - 2 k x - 2 x t + k^{2} + t^{2} + 2 k t

解答ステップ

(2 x - k)^{2} - 2 (2 x - k) (x + t) + (x + t)^{2}

(2 x - k)^{2} : 4 x^{2} - 4 k x + k^{2}

= 4 x^{2} - 4 k x + k^{2} - 2 (2 x - k) (x + t) + (x + t)^{2}

(x + t)^{2} : x^{2} + 2 x t + t^{2}

= 4 x^{2} - 4 k x + k^{2} - 2 (2 x - k) (x + t) + x^{2} + 2 x t + t^{2}

拡張

- 2 (2 x - k) (x + t) : - 4 x^{2} - 4 x t + 2 k x + 2 k t

= 4 x^{2} - 4 k x + k^{2} - 4 x^{2} - 4 x t + 2 k x + 2 k t + x^{2} + 2 x t + t^{2}

簡素化

4 x^{2} - 4 k x + k^{2} - 4 x^{2} - 4 x t + 2 k x + 2 k t + x^{2} + 2 x t + t^{2} : x^{2} - 2 k x - 2 x t + k^{2} + t^{2} + 2 k t

= x^{2} - 2 k x - 2 x t + k^{2} + t^{2} + 2 k t