展開する ((2+x)(3+2x)^2)/((1.8-2x)^2(1-2x)^2)

解

展開する

\frac{( 2 + x ) ( 3 + 2 x ) ^{2}}{( 1.8 - 2 x ) ^{2} ( 1 - 2 x ) ^{2}}

\frac{4 x ^{3} + 20 x ^{2} + 33 x + 18}{16 x ^{4} - 44.8 x ^{3} + 45.76 x ^{2} - 20.16 x + 3.24}

解答ステップ

\frac{( 2 + x ) ( 3 + 2 x ) ^{2}}{( 1.8 - 2 x ) ^{2} ( 1 - 2 x ) ^{2}}

(1.8 - 2 x)^{2} = 3.24 - 7.2 x + 4 x^{2}

= \frac{( x + 2 ) ( 2 x + 3 ) ^{2}}{( 4 x ^{2} - 7.2 x + 3.24 ) ( - 2 x + 1 ) ^{2}}

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

= \frac{( x + 2 ) ( 2 x + 3 ) ^{2}}{( 4 x ^{2} - 7.2 x + 3.24 ) ( 4 x ^{2} - 4 x + 1 )}

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

= \frac{( x + 2 ) ( 4 x ^{2} + 12 x + 9 )}{( 4 x ^{2} - 7.2 x + 3.24 ) ( 4 x ^{2} - 4 x + 1 )}

拡張

(3.24 - 7.2 x + 4 x^{2}) (1 - 4 x + 4 x^{2}) : 16 x^{4} - 44.8 x^{3} + 45.76 x^{2} - 20.16 x + 3.24

= \frac{( x + 2 ) ( 4 x ^{2} + 12 x + 9 )}{16 x ^{4} - 44.8 x ^{3} + 45.76 x ^{2} - 20.16 x + 3.24}

拡張

(2 + x) (9 + 12 x + 4 x^{2}) : 4 x^{3} + 20 x^{2} + 33 x + 18

= \frac{4 x ^{3} + 20 x ^{2} + 33 x + 18}{16 x ^{4} - 44.8 x ^{3} + 45.76 x ^{2} - 20.16 x + 3.24}