从 7x 2 – 4x 减去 5x 2 + 2x
算术是我们研究数字和运算符的数学分支，几何是我们研究形状和维度的分支，同样，代数是我们研究寻找未知值的数学分支。代数由数字、变量和算术运算运算符组成。具有常数值的项称为数字并用数字表示，没有常数值的项称为变量并用字母表示。
代数表达式
代数表达式是在数字、变量和运算符的帮助下将数学语句表示为数学项。例如：“从 5 中减去一个数的 4 倍”可以写为“5-4x”。
这里我们不知道unknown 的值，所以我们假设它为x。在表达式“5-4x”中，否定将表达式分为两个项。因此，根据项的数量，代数表达式分为以下几类。
- 单项式：如果表达式中的项数为 1，则该表达式称为单项式。示例：5x、3t 等。
- 二项式：如果表达式中的项数为两个，则该表达式称为二项式。示例：5a+2b、5e-6f 等。
- 三项式：如果一个表达式中有三个表达式，则该表达式称为三项式。示例：a+b+c、5q-r+6s 等。
- 多项式：如果表达式中的项数为一项或多项，则该表达式称为多项式。
Like and unlike terms
If the variable part of an expression is the same then the terms are known as the like terms and if the variable part of the expression is not the same then the terms are known as the, unlike terms.
Example: 8y² – 6y³ + 3y – 6y² – 3y³ – 18
In the above expression, 8y² and 6y² have the same variable, 6y³ and 3y³ have the same variable part, so these terms are known as like terms.
从 7x 2 – 4x 减去 5x 2 + 2x
解决方案：
Step to solve the problem:
Step 1: Write the statement in mathematical expression with the help of operators.
= (7x² – 4x) – (5x² + 2x)
Step 2: Open the bracket by distributive property of sign i.e. a – (b+c) = a – b – c
= 7x² – 4x – 5x² – 2x
Step 3: Do the operation on the like terms according to the sign.
= 2x² – 6x
Step 4: If there is a common factor in all the terms then take them out and write the expression in the simplest form.
= 2×x×x – 2×3×x
= 2x × (x – 3)
So the translation of 5x² + 2x subtracted from 7x² – 4x into the mathematical expression is 2x(x – 3).
类似问题
问题 1：从 6y² – 2y 减去 3y² + y。翻译成表达式。
解决方案：
Write the statement in mathematical expression with the help of operators.
= (6y² – 2y) – (3y² + y)
Open the bracket by distributive property of sign i.e. a – (b+c) = a – b – c
= 6y² – 2y – 3y² – y
Do the operation on the like terms according to the sign.
= 3y² – 3y
If there is a common factor in all the terms then take them out and write the expression in the simplest form.
= 3×y×y – 3×y
= 3y (y – 1)
So the translation of 3y² + y subtracted from 6y² – 2y is 3y(y – 1).
问题 2：从 9x² – x + 12 减去 3x² + x + 12。翻译成表达式。
解决方案：
Write the statement in mathematical expression with the help of operators.
= (9x² – x + 12) – (3x² + x + 12)
Open the bracket by distributive property of sign i.e. a – (b+c) = a – b – c
= 9x² – x + 12 – 3x² – x – 12
Do the operation on the like terms according to the sign.
= 6x² – 2x
If there is a common factor in all the terms then take them out and write the expression in the simplest form.
= 2×3×x×x – 2×x
= 2x(3x – 1)
So the translation of 3x² + x + 12 subtracted from 9x² – x + 12 is 2x(3x – 1).