expansion formula

简明释义

展开公式

英英释义

例句

1.In physics, the expansion formula 展开公式 aids in expressing laws of motion.

在物理学中，展开公式 expansion formula 有助于表达运动定律。

2.Using the expansion formula 展开公式, we can derive the area of complex shapes.

利用展开公式 expansion formula，我们可以推导出复杂形状的面积。

3.In algebra, the expansion formula 展开公式 helps in simplifying expressions.

在代数中，展开公式 expansion formula 有助于简化表达式。

4.The expansion formula 展开公式 is frequently used in calculus to expand functions.

在微积分中，展开公式 expansion formula 常用于扩展函数。

5.The expansion formula 展开公式 for binomials is essential for polynomial calculations.

二项式的展开公式 expansion formula 对多项式计算至关重要。

作文

The concept of an expansion formula is fundamental in various fields of mathematics, especially in algebra. An expansion formula allows us to express a polynomial or a mathematical expression in a more detailed and expanded form. This process not only simplifies complex equations but also provides insights into the relationships between different components of the expression. For instance, the binomial theorem is one of the most well-known expansion formulas. It states that for any positive integer n, the expansion of (a + b)^n can be expressed as a sum involving binomial coefficients. This theorem is not merely a theoretical construct; it has practical applications in probability, statistics, and even in computational algorithms.Understanding expansion formulas is crucial for students who wish to excel in mathematics. They serve as a bridge between basic algebraic concepts and more advanced topics, such as calculus and linear algebra. Mastery of expansion formulas enhances problem-solving skills, enabling students to tackle complex problems with greater ease. For example, when dealing with polynomial expressions, applying an expansion formula can simplify the process of finding roots or integrating functions.In addition to their academic importance, expansion formulas have real-world applications. Engineers and scientists often use these formulas to model physical phenomena. For instance, in physics, the expansion of trigonometric functions using Taylor series is a common practice. This allows for the approximation of functions that are otherwise difficult to compute, making calculations more manageable in practical scenarios.Moreover, the use of expansion formulas extends beyond pure mathematics. In economics, for example, expansion formulas can be used to analyze trends and make predictions based on historical data. By expanding certain economic models, analysts can better understand the underlying factors that drive market behavior, leading to more informed decision-making.In conclusion, the significance of expansion formulas cannot be overstated. They are essential tools in the mathematician's toolkit, facilitating a deeper understanding of various mathematical concepts and their applications. Whether in academia or industry, mastering expansion formulas opens doors to advanced study and practical problem-solving. As students and professionals alike continue to encounter increasingly complex mathematical challenges, a solid grasp of expansion formulas will undoubtedly prove beneficial in navigating these challenges effectively.

“展开公式”的概念在数学的各个领域中都是基础，尤其是在代数中。“展开公式”允许我们以更详细和扩展的形式表达多项式或数学表达式。这个过程不仅简化了复杂的方程，还提供了对表达式不同组成部分之间关系的深入理解。例如，二项式定理就是最著名的“展开公式”之一。它指出，对于任何正整数n，(a + b)^n的展开可以表示为包含二项式系数的和。这个定理不仅仅是一个理论构造；它在概率、统计甚至计算算法中都有实际应用。理解“展开公式”对于希望在数学上取得优异成绩的学生至关重要。它们在基础代数概念与更高级主题（如微积分和线性代数）之间架起了一座桥梁。掌握“展开公式”可以增强解决问题的能力，使学生能够更轻松地应对复杂问题。例如，在处理多项式表达式时，应用“展开公式”可以简化寻找根或积分函数的过程。除了学术重要性，“展开公式”还具有现实世界的应用。工程师和科学家经常使用这些公式来建模物理现象。例如，在物理学中，利用泰勒级数展开三角函数是一种常见做法。这使得对否则难以计算的函数进行近似，从而在实际场景中使计算变得更加可管理。此外，“展开公式”的使用超越了纯数学。在经济学中，例如，展开公式可以用于分析趋势并根据历史数据做出预测。通过展开某些经济模型，分析师可以更好地理解推动市场行为的潜在因素，从而做出更明智的决策。总之，“展开公式”的重要性不容小觑。它们是数学家工具箱中的基本工具，促进了对各种数学概念及其应用的更深入理解。无论是在学术界还是工业界，掌握“展开公式”都为高级学习和实际问题解决打开了大门。随着学生和专业人士继续面临日益复杂的数学挑战，扎实掌握“展开公式”无疑将在有效应对这些挑战中发挥重要作用。