Collecting Like Terms | 合并同类项

📚 Collecting Like Terms | 合并同类项

Simplifying expressions is one of the most important skills in algebra. By combining terms that have exactly the same variable part, you can turn a long expression into a shorter equivalent one.

化简表达式是代数中最重要的技能之一。通过合并变量部分完全相同的项，你可以把冗长的表达式化为更短的等价式。

1. What Is a Term? | 什么是”项”

In algebra, a term is either a number, a variable, or a product of numbers and variables. In the expression 4x² + 3x – 7, the terms are 4x², 3x, and -7.

在代数中，项可以是一个数、一个变量，或数与变量的乘积。在表达式 4x² + 3x – 7 中，各项是 4x²、3x 和 -7。

The number multiplying the variable is called the coefficient. In 4x², the coefficient is 4; in 3x, the coefficient is 3; and -7 is a constant term with no variable.

与变量相乘的数称为系数。在 4x² 中，系数是 4；在 3x 中，系数是 3；而 -7 是常数项，不含变量。

The sign of a term is part of it. In 3x – 2y + 5, the terms are 3x, -2y, and +5. This helps when collecting like terms.

项的符号是项的一部分。在 3x – 2y + 5 中，各项为 3x、-2y 和 +5。这对合并同类项有帮助。

2. What Are Like Terms? | 什么是同类项

Like terms are terms whose variable parts are identical, including the same powers. For example, 7x and 3x are like terms, while 2x and 2x² are not like terms.

同类项是变量部分完全相同的项，包括相同的指数。例如，7x 和 3x 是同类项，而 2x 和 2x² 不是同类项。

The order of variables does not matter: 2xy and 3yx are like terms because xy and yx represent the same product.

变量的顺序无关紧要：2xy 与 3yx 是同类项，因为 xy 与 yx 表示同一个乘积。

All constant terms are like terms with each other. So 5, -2, and 0.7 are like terms.

所有常数项彼此都是同类项。因此 5、-2 和 0.7 都是同类项。

3. The Rule for Combining | 合并规则

To collect like terms, add or subtract their coefficients only; keep the variable part exactly the same.

合并同类项时，只对系数进行加减；变量部分保持不变。

5x + 3x = (5 + 3)x = 8x

4a – 2a = (4 – 2)a = 2a

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