展開する (5x^2+2x+1)^3+ln(x+1)

解

展開する

(5 x^{2} + 2 x + 1)^{3} + ln (x + 1)

125 x^{6} + 150 x^{5} + 135 x^{4} + 68 x^{3} + 27 x^{2} + 6 x + 1 + ln (x + 1)

解答ステップ

(5 x^{2} + 2 x + 1)^{3} + ln (x + 1)

(5 x^{2} + 2 x + 1)^{3} = (5 x^{2} + 2 x + 1) (5 x^{2} + 2 x + 1) (5 x^{2} + 2 x + 1)

= (5 x^{2} + 2 x + 1) (5 x^{2} + 2 x + 1) (5 x^{2} + 2 x + 1) + ln (x + 1)

拡張

(5 x^{2} + 2 x + 1) (5 x^{2} + 2 x + 1) (5 x^{2} + 2 x + 1) : 125 x^{6} + 150 x^{5} + 135 x^{4} + 68 x^{3} + 27 x^{2} + 6 x + 1

= 125 x^{6} + 150 x^{5} + 135 x^{4} + 68 x^{3} + 27 x^{2} + 6 x + 1 + ln (x + 1)