展开 ((x+3)^4(x+5)^2)/((x+4)(x+1))

解答

展开

\frac{( x + 3 ) ^{4} ( x + 5 ) ^{2}}{( x + 4 ) ( x + 1 )}

\frac{x ^{6} + 22 x ^{5} + 199 x ^{4} + 948 x ^{3} + 2511 x ^{2} + 3510 x + 2025}{x ^{2} + 5 x + 4}

求解步骤

\frac{( x + 3 ) ^{4} ( x + 5 ) ^{2}}{( x + 4 ) ( x + 1 )}

(x + 3)^{4} = x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81

= \frac{( x ^{4} + 12 x ^{3} + 54 x ^{2} + 108 x + 81 ) ( x + 5 ) ^{2}}{( x + 4 ) ( x + 1 )}

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

= \frac{( x ^{4} + 12 x ^{3} + 54 x ^{2} + 108 x + 81 ) ( x ^{2} + 10 x + 25 )}{( x + 4 ) ( x + 1 )}

乘开

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

= \frac{( x ^{4} + 12 x ^{3} + 54 x ^{2} + 108 x + 81 ) ( x ^{2} + 10 x + 25 )}{x ^{2} + 5 x + 4}

乘开

(x^{4} + 12 x^{3} + 54 x^{2} + 108 x + 81) (x^{2} + 10 x + 25) : x^{6} + 22 x^{5} + 199 x^{4} + 948 x^{3} + 2511 x^{2} + 3510 x + 2025

= \frac{x ^{6} + 22 x ^{5} + 199 x ^{4} + 948 x ^{3} + 2511 x ^{2} + 3510 x + 2025}{x ^{2} + 5 x + 4}

e x p an d \frac{s + 1}{( s ^{2} + 2 s + 2 ) ^{2}}

e x p an d \frac{6 - 20 x}{15 x ( x + 1 )}

e x p an d \frac{( 3 x + 2 ) ^{2}}{9}

e x p an d \frac{2 x ^{2} - 9 x - 35}{( x + 1 ) ( x - 2 ) ( x + 3 )}

e x p an d \frac{6 x ^{2} - x + 1}{( x - 1 ) ( x + 2 ) ( x - 3 )}