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Algebraic Expressions__,__
Algebraic Expressions__,__
Variables
Algebraic Expressions__,__
Algebraic Expressions__,__
Constants
__ : 2x^2, 5y
__ : 2x^2, 5y
Monomials
2x + 3 = 3 + 2x__,__
2x + 3 = 3 + 2x__,__
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2(x + 3) = 2x + 6,__
2(x + 3) = 2x + 6,__
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2x + 3x =,
2x + 3x =,
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Study Notes
Algebraic Expressions
Definition
Algebraic expressions are mathematical phrases that combine variables, constants, and mathematical operations. They can be simplified, evaluated, and manipulated using algebraic rules.
Types of Algebraic Expressions
- Monomials: single-term expressions, e.g., 2x^2, 5y
- Binomials: two-term expressions, e.g., x + 3, 2x - 4
- Polynomials: expressions with multiple terms, e.g., x^2 + 3x - 2, 2x^3 - 5x^2 + x
Properties of Algebraic Expressions
- Commutative Property: the order of variables and constants does not change the result, e.g., 2x + 3 = 3 + 2x
- Associative Property: the order of operations does not change the result, e.g., (2x + 3) + 2 = 2x + (3 + 2)
- Distributive Property: a single value can be distributed to multiple terms, e.g., 2(x + 3) = 2x + 6
Simplifying Algebraic Expressions
- Combining Like Terms: combine terms with the same variable and coefficient, e.g., 2x + 3x = 5x
- Removing Parentheses: apply the distributive property to remove parentheses, e.g., 2(x + 3) = 2x + 6
Evaluating Algebraic Expressions
- Substitute values for variables to evaluate the expression, e.g., if x = 2, then 2x + 3 = 2(2) + 3 = 7
代数表达式定义
- 代数表达式是将变量、常数和数学运算符结合起来的数学短语
- 可以根据代数规则对其进行简化、求值和操作
代数表达式类型
- 单项式: 单个项的表达式，例如 2x^2、5y
- 二项式: 两个项的表达式，例如 x + 3、2x - 4
- 多项式: 多个项的表达式，例如 x^2 + 3x - 2、2x^3 - 5x^2 + x
代数表达式性质
- 交换性: 变量和常数的顺序不改变结果，例如 2x + 3 = 3 + 2x
- 结合性: 运算顺序不改变结果，例如 (2x + 3) + 2 = 2x + (3 + 2)
- 分布性: 单个值可以分布到多个项，例如 2(x + 3) = 2x + 6
简化代数表达式
- 合并同类项: 将具有相同变量和系数的项合并，例如 2x + 3x = 5x
- 去括号: 应用分布性来去除括号，例如 2(x + 3) = 2x + 6
评估代数表达式
- 将变量值代入表达式以评估结果，例如如果 x = 2，则 2x + 3 = 2(2) + 3 = 7
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Description
Algebraic Expressions
