乘法结合律 分配律 简便计算

2024年4月18日发(作者：)

乘法结合律 分配律 简便计算

英文回答：

The distributive property of multiplication over

addition states that for any three real numbers a, b, and c,

a(b + c) = ab + ac. This property can be used to simplify

expressions such as 3(x + 2) = 3x + 6.

The associative property of multiplication states that

for any three real numbers a, b, and c, (ab)c = a(bc). This

property can be used to simplify expressions such as

(2x)(3y) = 6xy.

The commutative property of multiplication states that

for any two real numbers a and b, ab = ba. This property

can be used to simplify expressions such as 3x 2 = 2 3x.

Here are some examples of how to use these properties

to simplify expressions:

3(x + 2) = 3x + 6 (distributive property)。

(2x)(3y) = 6xy (associative property)。

3x 2 = 2 3x (commutative property)。

These properties are very important in algebra and are

used extensively in solving equations and simplifying

expressions.

中文回答：

乘法结合律，对于任意三个实数 a、b 和 c，(ab)c = a(bc)。

此性质可用于简化诸如 (2x)(3y) = 6xy 的表达式。

乘法分配律，对于任意三个实数 a、b 和 c，a(b + c) = ab +

ac。此性质可用于简化诸如 3(x + 2) = 3x + 6 的表达式。

乘法交换律，对于任意两个实数 a 和 b，ab = ba。此性质可

用于简化诸如 3x 2 = 2 3x 的表达式。

以下是一些如何使用这些性质来简化表达式的示例：

3(x + 2) = 3x + 6（分配律）。

(2x)(3y) = 6xy（结合律）。

3x 2 = 2 3x（交换律）。

这些性质在代数中非常重要，并且在求解方程和简化表达式中

被广泛使用。