简化 7x 2 + 4.5y – 3y + x 2 – 5x
数学有不同的分支，其中一个分支是代数。在代数中，我们处理数字和变量。具有恒定值的项称为数字，没有恒定值的项称为变量。我们通常用数字表示数字，用字母表示变量。代数的主要用途是通过将未知数假设为字母或符号来找到它们。
代数表达式
代数表达式是数字、变量和算术运算运算符的组合。所有这些都以系统形式排列在一起，形成给定语句的数学表达式。例如，语句“从 15 中取出一个数字的六次”可以写为“15 – 6x”。在表达式 15 – 6x 中，减号将表达式分成两项。所以根据项的个数，代数表达式可以分为以下几种。
- 单项式：如果表达式中的项数为 1，则代数表达式称为单项式。示例：5x、8y 等
- 二项式：如果代数表达式中的项数为两项，则称为二项式表达式。示例：8t-9r、9a+2b 等。
- 三项式：如果代数表达式中有两项，则称为三项式。示例：5x+9y+3z、8a+3b-3c 等。
- 多项式：如果表达式中的项数为一项或多项，则称为多项式。
Like and unlike terms:
In an algebraic expression addition and subtraction is done only for like terms. In the expression, if the variable part of two or more different terms is the same then it is called like terms, and if the variable part is not the same then it is called, unlike terms.
Example: In the expression, 9x² + 25x -3x² -6y +3x + 7, 9x² and 3x² have the same variable, and 25x and 3x have the same variable and we name them like terms.
简化 7x 2 + 4.5y – 3y + x 2 – 5x
解决方案：
Step to solve the problem:
Step 1: Find out the like terms in the given algebraic expression.
= 7x² + 4.5y -3y +x² -5x
In the above expression, 7x² and x² have the same variable, 4.5y and 3y have the same variable.
= 7x² + x² +4.5y -3y -5x
Step 2: Do the calculation on like terms according to the arithmetic operators.
= 8x² +1.5y -5x
So the simplified form of 7x2 + 4.5y – 3y + x2 – 5x is 8x² +1.5y -5x.
类似问题
问题 1：简化 9x² + 25x -3x² -6y +3x + 7
解决方案：
In the given algebraic , find out the like terms.
= 9x² + 25x -3x² -6y +3x + 7
9x² and 3x² have same variable, and 25x and 3x have same variable.
= 9x² -3x² +25x +3x -6y +7
Do the calculation on like terms according to the arithmetic operators.
= 6x² +28x – 6y +7
Further this expression can not be solved because all the terms in the expression is unlike terms.
So the simplification of 9x² + 25x -3x² -6y +3x + 7 is 6x² +28x – 6y +7.
问题 2：化简：5x³ +3x² -6x + 9x² -5x³ +7
解决方案：
In the given algebraic , find out the like terms.
= 5x³ +3x² -6x + 9x² -5x³ +7
5x³ and 5x³ are like terms, 3x² and 9x² are like terms because they have same variables.
= 5x³ -5x³ +3x² +9x² -6x +7
Do the calculation on like terms according to the arithmetic operators.
= 0 + 12x² -6x +7
=12x² -6x +7
So the simplification of 5x³ +3x² -6x + 9x² -5x³ +7 is 12x² -6x +7.