展开 x^2(4(x-2)^3)

解答

展开

x^{2} (4 (x - 2)^{3})

4 x^{5} - 24 x^{4} + 48 x^{3} - 32 x^{2}

求解步骤

x^{2} (4 (x - 2)^{3})

去除括号:

(a) = a

= x^{2} \cdot 4 (x - 2)^{3}

(x - 2)^{3} = x^{3} - 6 x^{2} + 12 x - 8

= 4 x^{2} (x^{3} - 6 x^{2} + 12 x - 8)

= 4 x^{2} (x^{3} - 6 x^{2} + 12 x - 8)

打开括号

= x^{2} \cdot 4 x^{3} + x^{2} \cdot 4 (- 6 x^{2}) + x^{2} \cdot 4 \cdot 12 x + x^{2} \cdot 4 (- 8)

使用加减运算法则

+ (- a) = - a

= 4 x^{3} x^{2} - 4 \cdot 6 x^{2} x^{2} + 4 \cdot 12 x^{2} x - 4 \cdot 8 x^{2}

化简

4 x^{3} x^{2} - 4 \cdot 6 x^{2} x^{2} + 4 \cdot 12 x^{2} x - 4 \cdot 8 x^{2} : 4 x^{5} - 24 x^{4} + 48 x^{3} - 32 x^{2}

= 4 x^{5} - 24 x^{4} + 48 x^{3} - 32 x^{2}

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