展开 (x^2+4)^2*((x-1)/2)

解答

展开

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

\frac{( x - 1 ) x ^{4}}{2} + 4 x^{3} - 4 x^{2} + 8 x - 8

求解步骤

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

使用法则:

(a) = a

(\frac{x - 1}{2}) = \frac{x - 1}{2}

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

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

展开

(x^{2} + 4)^{2} : x^{4} + 8 x^{2} + 16

= \frac{x - 1}{2} (x^{4} + 8 x^{2} + 16)

使用分配律:

m (a + b + c) = ma + mb + m c

\frac{x - 1}{2} (x^{4} + 8 x^{2} + 16) = \frac{x - 1}{2} x^{4} + \frac{x - 1}{2} \cdot 8 x^{2} + \frac{x - 1}{2} \cdot 16

= \frac{x - 1}{2} x^{4} + \frac{x - 1}{2} \cdot 8 x^{2} + \frac{x - 1}{2} \cdot 16

化简

\frac{x - 1}{2} x^{4} + \frac{x - 1}{2} \cdot 8 x^{2} + \frac{x - 1}{2} \cdot 16 : \frac{( x - 1 ) x ^{4}}{2} + 4 x^{3} - 4 x^{2} + 8 x - 8

= \frac{( x - 1 ) x ^{4}}{2} + 4 x^{3} - 4 x^{2} + 8 x - 8

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