减法和简化 (0.04x 3 -0.03x 2 +0.02x) – (0.03x 3 +0.08x 2 -6)
数学基本上分为不同的分支，其中一个分支是代数。在代数中，人们处理数字和变量，已知值称为数字，未知值称为变量。变量可以取任何值。加法、减法、乘法和除法等算术运算也应用于代数中，以找出未知数的值。
代数表达式
代数表达式是按系统顺序排列的数字和变量的组合。数字和变量通过四个基本的数学运算符，加法、减法、乘法或除法相关联。示例：通过使用两个数字（5 和 6）和一个变量 x，可以形成代数表达式 6x + 5。在这个表达式中，有两项。因此，根据项数代数表达式分为以下类型，
- 单项式：当代数表达式只有一项时，则称为单项式。示例：5t、8y 等
- 二项式：当代数表达式中的项数为两个时，该表达式称为二项式。示例：5t – 8k、8t + 6 等
- 三项式：具有三项的代数表达式称为三项式。示例：6x – 3y – 5z、9t – 6u + 7w 等
- 多项式：具有一项或多项的代数表达式称为多项式。
要在代数表达式中执行基本的算术运算，请找出相似项和不同项。
Like and Unlike Terms: The term having same variables are known as like terms and the terms which does not have same variable is known as unlike terms.
Example: In the algebraic expression, 5x +6y -7x² -4x +9, the terms which have same variables are 5x and 4x, so these two terms is called as like terms.
减法和简化：(0.04x 3 – 0.03x 2 + 0.02x) – (0.03x 3 + 0.08x 2 – 6)
解决方案：
Steps to solve the problem
Step 1: Find out the like terms of the given algebraic expression.
Step 2: Apply the arithmetic operation on the numeral part of like terms.
Step 3: No operation is applied on unlike terms.
Step 4: By solving the like term, reduce the expression in the lowest term.
In the given algebraic expression, like terms are 0.04x³ and 0.03x³, 0.03x² and 0.08x².
The given expression can be written as,
= 0.04x³ – 0.03x² + 0.02x – 0.03x³ – 0.08x² + 6
= 0.04x³ – 0.03x³ – 0.03x² – 0.08x² + 0.02x + 6
On solving like terms,
= 0.01x³ – 0.11x² + 0.02x + 6
On simplifying the expression (0.04x³ – 0.03x² + 0.02x) – ( 0.03x³ + 0.08x² – 6), we got 0.01x³ – 0.11x² + 0.02x + 6.
类似问题
问题 1：减法和简化：(5x³ – 12x² – 6x + 12) – (12x² +6x – 10)
解决方案：
In the given expression like terms are 12x² and 12x², 6x and 6x, 12 and 10.
The given expression can be written as
= 5x³ – 12x² – 6x + 12 – 12x² – 6x +10
= 5x³ – 12x² – 12x² – 6x – 6x +12 +10
On solving the like terms,
= 5x³ – 24x² – 12x + 22
So, on simplifying the expression (5x³ – 12x² – 6x + 12) – (12x² + 6x – 10),
= 5x³ – 24x² – 12x + 22.
问题 2：减法和简化：(0.5y³ – 0.03x² – 0.3z + 12) – (0.4y³ – 0.36x² + 0.2z – 11)
解决方案：
In the given expression, like terms are 0.5y³ and 0.4y³, 0.03x² and 0.36x², and 0.3z and 0.2z, 12 and 11
The given expression can be written as,
= 0.5y³ – 0.03x² – 0.3z +12 – 0.4y³ + 0.36x² – 0.2z +11
= 0.5y³ – 0.4y³ – 0.03x² + 0.36x² – 0.3z – 0.2z + 12 + 11
On solving the like terms,
= 0.1y³ + 0.06x² – 0.5z + 23
So, on solving the expression (0.5y³ – 0.03x² – 0.3z + 12) – (0.4y³ – 0.36x² + 0.2z -11),
= 0.1y³ + 0.06x² – 0.5z + 23