代数示例

${(2 x^{3} + 3 y^{2})}^{7}$

解题步骤 1

帕斯卡三角形可以显示为：

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

$1 - 5 - 10 - 10 - 5 - 1$

$1 - 6 - 15 - 20 - 15 - 6 - 1$

$1 - 7 - 21 - 35 - 35 - 21 - 7 - 1$

通过取指数 $n$ 并和 $1$ 相加，该三角形可用于计算 ${(a + b)}^{n}$ 的展开系数。这些系数将对应三角形的直线 $n + 1$ 。因为 ${(2 x^{3} + 3 y^{2})}^{7}$ , $n = 7$ ，所以展开系数将对应直线 $8$ 。

解题步骤 2

展开式符合这个规则 ${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ 。从三角形可以得出它的系数值为 $1 - 7 - 21 - 35 - 35 - 21 - 7 - 1$ 。

$1 a^{7} b^{0} + 7 a^{6} b + 21 a^{5} b^{2} + 35 a^{4} b^{3} + 35 a^{3} b^{4} + 21 a^{2} b^{5} + 7 a b^{6} + 1 a^{0} b^{7}$

解题步骤 3

将 $a$ $2 x^{3}$ 和 $b$ $3 y^{2}$ 的实际值代入表达式。

$1 {(2 x^{3})}^{7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4

化简每一项。

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解题步骤 4.1

将 ${(2 x^{3})}^{7}$ 乘以 $1$ 。

${(2 x^{3})}^{7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.2

对 $2 x^{3}$ 运用乘积法则。

$2^{7} {(x^{3})}^{7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.3

对 $2$ 进行 $7$ 次方运算。

$128 {(x^{3})}^{7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.4

将 ${(x^{3})}^{7}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.4.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{3 \cdot 7} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.4.2

将 $3$ 乘以 $7$ 。

$128 x^{21} {(3 y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.5

对 $3 y^{2}$ 运用乘积法则。

$128 x^{21} (3^{0} {(y^{2})}^{0}) + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.6

使用乘法的交换性质重写。

$128 \cdot 3^{0} x^{21} {(y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.7

任何数的 $0$ 次方都是 $1$ 。

$128 \cdot 1 x^{21} {(y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.8

将 $128$ 乘以 $1$ 。

$128 x^{21} {(y^{2})}^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.9

将 ${(y^{2})}^{0}$ 中的指数相乘。

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解题步骤 4.9.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} y^{2 \cdot 0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.9.2

将 $2$ 乘以 $0$ 。

$128 x^{21} y^{0} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.10

任何数的 $0$ 次方都是 $1$ 。

$128 x^{21} \cdot 1 + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.11

将 $128$ 乘以 $1$ 。

$128 x^{21} + 7 {(2 x^{3})}^{6} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.12

对 $2 x^{3}$ 运用乘积法则。

$128 x^{21} + 7 (2^{6} {(x^{3})}^{6}) {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.13

对 $2$ 进行 $6$ 次方运算。

$128 x^{21} + 7 (64 {(x^{3})}^{6}) {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.14

将 ${(x^{3})}^{6}$ 中的指数相乘。

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解题步骤 4.14.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 7 (64 x^{3 \cdot 6}) {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.14.2

将 $3$ 乘以 $6$ 。

$128 x^{21} + 7 (64 x^{18}) {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.15

将 $64$ 乘以 $7$ 。

$128 x^{21} + 448 x^{18} {(3 y^{2})}^{1} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.16

化简。

$128 x^{21} + 448 x^{18} (3 y^{2}) + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.17

使用乘法的交换性质重写。

$128 x^{21} + 448 \cdot 3 x^{18} y^{2} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.18

将 $448$ 乘以 $3$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 21 {(2 x^{3})}^{5} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.19

对 $2 x^{3}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 21 (2^{5} {(x^{3})}^{5}) {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.20

对 $2$ 进行 $5$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 21 (32 {(x^{3})}^{5}) {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.21

将 ${(x^{3})}^{5}$ 中的指数相乘。

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解题步骤 4.21.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 21 (32 x^{3 \cdot 5}) {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.21.2

将 $3$ 乘以 $5$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 21 (32 x^{15}) {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.22

将 $32$ 乘以 $21$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 672 x^{15} {(3 y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.23

对 $3 y^{2}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 672 x^{15} (3^{2} {(y^{2})}^{2}) + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.24

使用乘法的交换性质重写。

$128 x^{21} + 1344 x^{18} y^{2} + 672 \cdot 3^{2} x^{15} {(y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.25

对 $3$ 进行 $2$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 672 \cdot 9 x^{15} {(y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.26

将 $672$ 乘以 $9$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} {(y^{2})}^{2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.27

将 ${(y^{2})}^{2}$ 中的指数相乘。

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解题步骤 4.27.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{2 \cdot 2} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.27.2

将 $2$ 乘以 $2$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 {(2 x^{3})}^{4} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.28

对 $2 x^{3}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 (2^{4} {(x^{3})}^{4}) {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.29

对 $2$ 进行 $4$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 (16 {(x^{3})}^{4}) {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.30

将 ${(x^{3})}^{4}$ 中的指数相乘。

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解题步骤 4.30.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 (16 x^{3 \cdot 4}) {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.30.2

将 $3$ 乘以 $4$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 35 (16 x^{12}) {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.31

将 $16$ 乘以 $35$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 560 x^{12} {(3 y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.32

对 $3 y^{2}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 560 x^{12} (3^{3} {(y^{2})}^{3}) + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.33

使用乘法的交换性质重写。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 560 \cdot 3^{3} x^{12} {(y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.34

对 $3$ 进行 $3$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 560 \cdot 27 x^{12} {(y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.35

将 $560$ 乘以 $27$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} {(y^{2})}^{3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.36

将 ${(y^{2})}^{3}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.36.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{2 \cdot 3} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.36.2

将 $2$ 乘以 $3$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 {(2 x^{3})}^{3} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.37

对 $2 x^{3}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 (2^{3} {(x^{3})}^{3}) {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.38

对 $2$ 进行 $3$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 (8 {(x^{3})}^{3}) {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.39

将 ${(x^{3})}^{3}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.39.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 (8 x^{3 \cdot 3}) {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.39.2

将 $3$ 乘以 $3$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 35 (8 x^{9}) {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.40

将 $8$ 乘以 $35$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 280 x^{9} {(3 y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.41

对 $3 y^{2}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 280 x^{9} (3^{4} {(y^{2})}^{4}) + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.42

使用乘法的交换性质重写。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 280 \cdot 3^{4} x^{9} {(y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.43

对 $3$ 进行 $4$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 280 \cdot 81 x^{9} {(y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.44

将 $280$ 乘以 $81$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} {(y^{2})}^{4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.45

将 ${(y^{2})}^{4}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.45.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{2 \cdot 4} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.45.2

将 $2$ 乘以 $4$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 {(2 x^{3})}^{2} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.46

对 $2 x^{3}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 (2^{2} {(x^{3})}^{2}) {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.47

对 $2$ 进行 $2$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 (4 {(x^{3})}^{2}) {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.48

将 ${(x^{3})}^{2}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.48.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 (4 x^{3 \cdot 2}) {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.48.2

将 $3$ 乘以 $2$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 21 (4 x^{6}) {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.49

将 $4$ 乘以 $21$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 84 x^{6} {(3 y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.50

对 $3 y^{2}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 84 x^{6} (3^{5} {(y^{2})}^{5}) + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.51

使用乘法的交换性质重写。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 84 \cdot 3^{5} x^{6} {(y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.52

对 $3$ 进行 $5$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 84 \cdot 243 x^{6} {(y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.53

将 $84$ 乘以 $243$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} {(y^{2})}^{5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.54

将 ${(y^{2})}^{5}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.54.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{2 \cdot 5} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.54.2

将 $2$ 乘以 $5$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 7 {(2 x^{3})}^{1} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.55

化简。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 7 (2 x^{3}) {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.56

将 $2$ 乘以 $7$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 14 x^{3} {(3 y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.57

对 $3 y^{2}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 14 x^{3} (3^{6} {(y^{2})}^{6}) + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.58

使用乘法的交换性质重写。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 14 \cdot 3^{6} x^{3} {(y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.59

对 $3$ 进行 $6$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 14 \cdot 729 x^{3} {(y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.60

将 $14$ 乘以 $729$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} {(y^{2})}^{6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.61

将 ${(y^{2})}^{6}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.61.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{2 \cdot 6} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.61.2

将 $2$ 乘以 $6$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 1 {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.62

将 ${(2 x^{3})}^{0}$ 乘以 $1$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + {(2 x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.63

对 $2 x^{3}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 2^{0} {(x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.64

任何数的 $0$ 次方都是 $1$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 1 {(x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.65

将 ${(x^{3})}^{0}$ 乘以 $1$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + {(x^{3})}^{0} {(3 y^{2})}^{7}$

解题步骤 4.66

将 ${(x^{3})}^{0}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.66.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + x^{3 \cdot 0} {(3 y^{2})}^{7}$

解题步骤 4.66.2

将 $3$ 乘以 $0$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + x^{0} {(3 y^{2})}^{7}$

解题步骤 4.67

任何数的 $0$ 次方都是 $1$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 1 {(3 y^{2})}^{7}$

解题步骤 4.68

将 ${(3 y^{2})}^{7}$ 乘以 $1$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + {(3 y^{2})}^{7}$

解题步骤 4.69

对 $3 y^{2}$ 运用乘积法则。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 3^{7} {(y^{2})}^{7}$

解题步骤 4.70

对 $3$ 进行 $7$ 次方运算。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 2187 {(y^{2})}^{7}$

解题步骤 4.71

将 ${(y^{2})}^{7}$ 中的指数相乘。

点击获取更多步骤...

解题步骤 4.71.1

运用幂法则并将指数相乘， ${(a^{m})}^{n} = a^{m n}$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 2187 y^{2 \cdot 7}$

解题步骤 4.71.2

将 $2$ 乘以 $7$ 。

$128 x^{21} + 1344 x^{18} y^{2} + 6048 x^{15} y^{4} + 15120 x^{12} y^{6} + 22680 x^{9} y^{8} + 20412 x^{6} y^{10} + 10206 x^{3} y^{12} + 2187 y^{14}$

代数 示例

代数示例