like terms

简明释义

同类项

英英释义

例句

1.You need to combine all like terms 同类项 before you can solve the problem.

在解决问题之前，你需要先合并所有的同类项。

2.In the expression 3x + 5x, the terms are like terms 同类项 because they both contain x.

在表达式3x + 5x中，这些项是同类项，因为它们都包含x。

3.When solving equations, remember to group like terms 同类项 together.

在解方程时，记得将同类项放在一起。

4.To factor the polynomial, first identify the like terms 同类项 that can be combined.

要对多项式进行因式分解，首先识别可以合并的同类项。

5.In algebra, you can only combine like terms 同类项 to simplify expressions.

在代数中，你只能合并同类项来简化表达式。

作文

In mathematics, particularly in algebra, the concept of like terms is fundamental for simplifying expressions and solving equations. Like terms are terms that contain the same variable raised to the same power. For example, in the expression 3x + 5x, both terms are considered like terms because they both have the variable x raised to the first power. On the other hand, terms such as 2x and 3y are not like terms since they involve different variables.Understanding like terms is crucial when performing operations such as addition or subtraction. When we combine like terms, we simply add or subtract their coefficients. In the previous example, 3x + 5x can be simplified to 8x, which is a more concise representation of the same quantity. This process of combining like terms helps to streamline calculations and makes it easier to work with algebraic expressions.Moreover, recognizing like terms plays a significant role in solving equations. For instance, consider the equation 2x + 3x - 4 = 10. To solve for x, we first combine the like terms on the left side of the equation. This results in 5x - 4 = 10. Next, we isolate the variable by adding 4 to both sides, yielding 5x = 14. Finally, dividing both sides by 5 gives us x = 14/5, or 2.8. This example illustrates how identifying like terms can simplify the process of solving equations and lead to quicker solutions.In addition to aiding in simplification and solving equations, like terms also help in understanding polynomial functions. A polynomial is an expression that consists of variables raised to non-negative integer powers and their coefficients. For example, the polynomial 4x^3 + 3x^2 - 2x + 7 contains several like terms. Here, 4x^3 is a term of degree 3, 3x^2 is of degree 2, and -2x is of degree 1. Each term contributes to the overall shape and behavior of the polynomial function.Furthermore, when graphing polynomials, understanding like terms allows us to identify key features such as intercepts and turning points. For example, if we want to find the roots of the polynomial equation, we need to set the polynomial equal to zero and solve for the variable. This often involves combining like terms to form a simpler equation that is easier to analyze.In conclusion, the concept of like terms is essential in algebra. It facilitates the simplification of expressions, aids in solving equations, and enhances our understanding of polynomial functions. Mastering the identification and manipulation of like terms can greatly improve one's mathematical skills, allowing for more efficient problem-solving and a deeper comprehension of algebraic concepts. As students progress in their studies, they will find that the ability to work with like terms is not only beneficial but necessary for success in higher-level mathematics. Therefore, investing time in understanding like terms will undoubtedly pay off in the long run, paving the way for greater achievements in the field of mathematics.

在数学中，特别是在代数中，同类项的概念对于简化表达式和解决方程是至关重要的。同类项是指包含相同变量且指数相同的项。例如，在表达式3x + 5x中，这两个项被认为是同类项，因为它们都有变量x，且指数为1。另一方面，像2x和3y这样的项则不是同类项，因为它们涉及不同的变量。理解同类项在进行加法或减法等运算时至关重要。当我们合并同类项时，只需将它们的系数相加或相减。在前面的例子中，3x + 5x可以简化为8x，这是同一数量更简洁的表示。这种合并同类项的过程有助于简化计算，使得处理代数表达式变得更加容易。此外，识别同类项在解方程中也起着重要作用。例如，考虑方程2x + 3x - 4 = 10。要解出x，我们首先在方程的左侧合并同类项。这导致5x - 4 = 10。接下来，我们通过在两边都加4来隔离变量，从而得到5x = 14。最后，将两边都除以5，我们得到x = 14/5，或2.8。这个例子说明了识别同类项如何简化解方程的过程，并导致更快的解决方案。除了帮助简化和解方程外，同类项还帮助我们理解多项式函数。多项式是由变量的非负整数幂及其系数组成的表达式。例如，多项式4x^3 + 3x^2 - 2x + 7包含几个同类项。在这里，4x^3是一个3次项，3x^2是2次项，而-2x是1次项。每个项都对多项式函数的整体形状和行为产生影响。此外，在绘制多项式图形时，理解同类项使我们能够识别关键特征，例如截距和转折点。例如，如果我们想找到多项式方程的根，我们需要将多项式设为零并解出变量。这通常涉及合并同类项以形成更简单的方程，使其更易于分析。总之，同类项的概念在代数中是必不可少的。它促进了表达式的简化，帮助解方程，并增强了我们对多项式函数的理解。掌握识别和操作同类项的能力可以极大地提高一个人的数学技能，使问题解决更加高效，并深化对代数概念的理解。随着学生学习的深入，他们会发现与同类项打交道的能力不仅有益，而且在高层次数学中是必要的。因此，投入时间理解同类项无疑会在长远中获得回报，为在数学领域取得更大的成就铺平道路。