展開する (3(3x^2-2)^2(6x^2+18x+4))/((2x+3)^4)

解

展開する

\frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{( 2 x + 3 ) ^{4}}

\frac{162 x ^{6} + 486 x ^{5} - 108 x ^{4} - 648 x ^{3} - 72 x ^{2} + 216 x + 48}{16 x ^{4} + 96 x ^{3} + 216 x ^{2} + 216 x + 81}

解答ステップ

\frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{( 2 x + 3 ) ^{4}}

(2 x + 3)^{4} = 16 x^{4} + 96 x^{3} + 216 x^{2} + 216 x + 81

= \frac{3 ( 3 x ^{2} - 2 ) ^{2} ( 6 x ^{2} + 18 x + 4 )}{16 x ^{4} + 96 x ^{3} + 216 x ^{2} + 216 x + 81}

(3 x^{2} - 2)^{2} = 9 x^{4} - 12 x^{2} + 4

= \frac{3 ( 9 x ^{4} - 12 x ^{2} + 4 ) ( 6 x ^{2} + 18 x + 4 )}{16 x ^{4} + 96 x ^{3} + 216 x ^{2} + 216 x + 81}

拡張

3 (9 x^{4} - 12 x^{2} + 4) (6 x^{2} + 18 x + 4) : 162 x^{6} + 486 x^{5} - 108 x^{4} - 648 x^{3} - 72 x^{2} + 216 x + 48

= \frac{162 x ^{6} + 486 x ^{5} - 108 x ^{4} - 648 x ^{3} - 72 x ^{2} + 216 x + 48}{16 x ^{4} + 96 x ^{3} + 216 x ^{2} + 216 x + 81}