展開する ((2x+3)^2(x-2)^5)/(x^3(x-5)^2)

解

展開する

\frac{( 2 x + 3 ) ^{2} ( x - 2 ) ^{5}}{x ^{3} ( x - 5 ) ^{2}}

\frac{4 x ^{7} - 28 x ^{6} + 49 x ^{5} + 70 x ^{4} - 280 x ^{3} + 112 x ^{2} + 336 x - 288}{x ^{5} - 10 x ^{4} + 25 x ^{3}}

解答ステップ

\frac{( 2 x + 3 ) ^{2} ( x - 2 ) ^{5}}{x ^{3} ( x - 5 ) ^{2}}

(x - 5)^{2} = x^{2} - 10 x + 25

= \frac{( 2 x + 3 ) ^{2} ( x - 2 ) ^{5}}{x ^{3} ( x ^{2} - 10 x + 25 )}

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

= \frac{( 4 x ^{2} + 12 x + 9 ) ( x - 2 ) ^{5}}{x ^{3} ( x ^{2} - 10 x + 25 )}

(x - 2)^{5} = x^{5} - 10 x^{4} + 40 x^{3} - 80 x^{2} + 80 x - 32

= \frac{( 4 x ^{2} + 12 x + 9 ) ( x ^{5} - 10 x ^{4} + 40 x ^{3} - 80 x ^{2} + 80 x - 32 )}{x ^{3} ( x ^{2} - 10 x + 25 )}

拡張

x^{3} (x^{2} - 10 x + 25) : x^{5} - 10 x^{4} + 25 x^{3}

= \frac{( 4 x ^{2} + 12 x + 9 ) ( x ^{5} - 10 x ^{4} + 40 x ^{3} - 80 x ^{2} + 80 x - 32 )}{x ^{5} - 10 x ^{4} + 25 x ^{3}}

拡張

(4 x^{2} + 12 x + 9) (x^{5} - 10 x^{4} + 40 x^{3} - 80 x^{2} + 80 x - 32) : 4 x^{7} - 28 x^{6} + 49 x^{5} + 70 x^{4} - 280 x^{3} + 112 x^{2} + 336 x - 288

= \frac{4 x ^{7} - 28 x ^{6} + 49 x ^{5} + 70 x ^{4} - 280 x ^{3} + 112 x ^{2} + 336 x - 288}{x ^{5} - 10 x ^{4} + 25 x ^{3}}