展開する ((1-3x^2)^2(x^2+3))/((2x+1)^2(x^3-1))

解

展開する

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

\frac{9 x ^{6} + 21 x ^{4} - 17 x ^{2} + 3}{4 x ^{5} - 4 x ^{2} + 4 x ^{4} - 4 x + x ^{3} - 1}

解答ステップ

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

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

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

(1 - 3 x^{2})^{2} = 1 - 6 x^{2} + 9 x^{4}

= \frac{( 9 x ^{4} - 6 x ^{2} + 1 ) ( x ^{2} + 3 )}{( 4 x ^{2} + 4 x + 1 ) ( x ^{3} - 1 )}

拡張

(4 x^{2} + 4 x + 1) (x^{3} - 1) : 4 x^{5} - 4 x^{2} + 4 x^{4} - 4 x + x^{3} - 1

= \frac{( 9 x ^{4} - 6 x ^{2} + 1 ) ( x ^{2} + 3 )}{4 x ^{5} - 4 x ^{2} + 4 x ^{4} - 4 x + x ^{3} - 1}

拡張

(1 - 6 x^{2} + 9 x^{4}) (x^{2} + 3) : 9 x^{6} + 21 x^{4} - 17 x^{2} + 3

= \frac{9 x ^{6} + 21 x ^{4} - 17 x ^{2} + 3}{4 x ^{5} - 4 x ^{2} + 4 x ^{4} - 4 x + x ^{3} - 1}