展開する 3((x+1)^2(x-1)^2)

解

展開する

3 ((x + 1)^{2} (x - 1)^{2})

3 x^{4} - 6 x^{2} + 3

解答ステップ

3 ((x + 1)^{2} (x - 1)^{2})

括弧を削除する:

(a) = a

= 3 (x + 1)^{2} (x - 1)^{2}

(x + 1)^{2} = x^{2} + 2 x + 1

= 3 (x^{2} + 2 x + 1) (x - 1)^{2}

(x - 1)^{2} = x^{2} - 2 x + 1

= 3 (x^{2} + 2 x + 1) (x^{2} - 2 x + 1)

拡張

(x^{2} + 2 x + 1) (x^{2} - 2 x + 1) : x^{4} - 2 x^{2} + 1

= 3 (x^{4} - 2 x^{2} + 1)

拡張

3 (x^{4} - 2 x^{2} + 1) : 3 x^{4} - 6 x^{2} + 3

= 3 x^{4} - 6 x^{2} + 3