簡約 ((((x+1)^4-4))/(4(x+1)^2))^2

解

簡約

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

\frac{( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x - 3 ) ^{2}}{16 ( x + 1 ) ^{4}}

解答ステップ

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

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

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

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

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

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

4^{2} = 16

= \frac{( x ^{4} + 4 x ^{3} + 6 x ^{2} + 4 x - 3 ) ^{2}}{16 ( x + 1 ) ^{4}}