binomial expression

简明释义

二项式;

英英释义

例句

1.The formula for the square of a binomial expression 二项式表达式 is (a + b)² = a² + 2ab + b².

一个binomial expression 二项式表达式的平方公式是 (a + b)² = a² + 2ab + b²。

2.In algebra, a binomial expression 二项式表达式 consists of two terms separated by a plus or minus sign.

在代数中，binomial expression 二项式表达式由两个项通过加号或减号分隔组成。

3.In probability, the binomial expression 二项式表达式 represents the number of successes in a fixed number of trials.

在概率论中，binomial expression 二项式表达式表示在固定次数试验中的成功次数。

4.To factor a binomial expression 二项式表达式, look for common factors in both terms.

要对一个binomial expression 二项式表达式进行因式分解，请寻找两个项中的共同因子。

5.The binomial expression 二项式表达式 x² - 4 can be factored into (x - 2)(x + 2).

这个binomial expression 二项式表达式 x² - 4 可以被分解为 (x - 2)(x + 2)。

作文

In the realm of mathematics, particularly in algebra, understanding various expressions is crucial for problem-solving and mathematical reasoning. One such important type of expression is the binomial expression, which consists of two terms connected by either a plus or a minus sign. For example, the expression 'x + y' is a classic instance of a binomial expression. These expressions are fundamental because they serve as building blocks for more complex equations and functions.The significance of binomial expressions extends beyond mere definitions; they play a vital role in various mathematical operations, including addition, subtraction, multiplication, and even division. When we multiply two binomial expressions, we often use the distributive property, commonly referred to as the FOIL method (First, Outside, Inside, Last). This technique allows us to systematically multiply each term of one binomial by each term of the other, ensuring that no part of the expression is overlooked.For instance, consider the multiplication of the binomial expressions (a + b) and (c + d). Using the FOIL method, we would calculate: 1. First: a * c 2. Outside: a * d 3. Inside: b * c 4. Last: b * d Thus, the product would be ac + ad + bc + bd, demonstrating how binomial expressions can combine to form more complex polynomial expressions.Moreover, binomial expressions are frequently encountered in real-world applications, such as calculating areas, volumes, and in various fields like physics and engineering. For example, if an engineer needs to determine the area of a rectangular plot of land where the length is represented by the binomial expression (x + 5) meters and the width is (x + 3) meters, they would multiply these two binomial expressions to find the area: (x + 5)(x + 3) = x² + 8x + 15 square meters. This showcases how binomial expressions can model real-life scenarios effectively.Additionally, the binomial theorem is a powerful tool that expands binomial expressions raised to a power. It states that (a + b)ⁿ can be expanded into a series involving coefficients known as binomial coefficients. This theorem is not only a theoretical concept but also has practical applications in probability and statistics, where it helps in calculating combinations and permutations.To summarize, the binomial expression is a foundational element in algebra that facilitates various mathematical operations and real-world applications. Its importance cannot be overstated, as it is integral to understanding more complex mathematical concepts and solving real-life problems. Whether you are a student grappling with algebra or a professional applying mathematical principles in your field, mastering binomial expressions is essential for success. As we continue to explore the vast landscape of mathematics, the binomial expression will remain a key player in our mathematical toolkit, enabling us to tackle challenges with confidence and precision.

在数学的领域，特别是代数中，理解各种表达式对于解决问题和数学推理至关重要。其中一种重要的表达式是二项式表达式，它由两个用加号或减号连接的项组成。例如，表达式'x + y'就是一个经典的二项式表达式实例。这些表达式是基础，因为它们作为更复杂的方程和函数的构建块。二项式表达式的重要性不仅仅在于定义；它们在包括加法、减法、乘法甚至除法等各种数学运算中发挥着至关重要的作用。当我们将两个二项式表达式相乘时，我们通常使用分配律，通常称为FOIL方法（首项、外项、内项、末项）。这个技巧使我们能够系统地将一个二项式的每个项与另一个的每个项相乘，确保没有部分被忽视。例如，考虑二项式表达式(a + b)与(c + d)的乘法。使用FOIL方法，我们将计算：1. 首项：a * c 2. 外项：a * d 3. 内项：b * c 4. 末项：b * d 因此，积将是ac + ad + bc + bd，展示了如何将二项式表达式组合成更复杂的多项式表达式。此外，二项式表达式在现实世界的应用中经常出现，例如计算面积、体积，以及在物理和工程等各个领域中。例如，如果一位工程师需要确定一块矩形土地的面积，其长度由二项式表达式(x + 5)米表示，而宽度为(x + 3)米，他们将乘以这两个二项式表达式以找到面积：(x + 5)(x + 3) = x² + 8x + 15平方米。这展示了二项式表达式如何有效地模拟现实生活场景。此外，二项式定理是一个强大的工具，它扩展了提升到某个幂的二项式表达式。它指出(a + b)ⁿ可以扩展为涉及称为二项系数的系数的级数。这个定理不仅是一个理论概念，而且在概率和统计中具有实际应用，有助于计算组合和排列。总之，二项式表达式是代数中的一个基础元素，促进了各种数学运算和现实世界应用。其重要性不容小觑，因为它对理解更复杂的数学概念和解决现实问题至关重要。无论你是一个正在努力学习代数的学生，还是一个在自己的领域应用数学原理的专业人士，掌握二项式表达式对于成功都是至关重要的。当我们继续探索数学的广阔领域时，二项式表达式将仍然是我们数学工具箱中的关键角色，使我们能够自信而精准地应对挑战。