从 (3x 2 +4x–6) 中减去 (2x 2 –5x+7)
数学分为不同的部分，其中一个部分是代数。在代数中，我们使用数字和变量。具有常数值的项称为数字，没有任何常数值的项称为变量。数字和变量通过算术运算运算符加法、减法、乘法和除法连接起来。对于未知数的计算，我们相应地应用算术运算并得到答案。
代数表达式
An algebraic expression is the combination of numerals and variables with the help of basic arithmetic operators like addition, subtraction, multiplication, or division. An algebraic expression is a mathematical form of writing a mathematical statement. It consists of numerals and variables along with arithmetic operators. The term which has constant value is termed as the numerals and the term which does not have constant value s termed as the variables.
For example,
‘A number is increased by 7’ can be written as the algebraic term ‘x + 7’
Here x is unknown, it can take any value and 7 is a fixed value. It is separated by + sign into two terms. On the basis of the number of terms, an algebraic expression can be divided into the following categories.
- 单项式：如果代数表达式中的项数为一个，则称为单项式。示例：9x、6a 等
- 二项式：如果代数表达式中的项数为两个，则代数表达式称为二项式表达式。示例：8x+3y、9y+6z 等。
- 三项式：如果代数表达式中的项数为三，则代数表达式称为三项式。示例：6a+3b+9c、6x+2y+3 等。
- 多项式：如果代数表达式中的项数为一项或多于一项，则该代数表达式称为多项式。
Like and Unlike terms:
In an algebraic expression, if the variable part is the same then we call them like terms and if the variable part is not the same then we call it unlike terms. Addition and subtraction are done on the basis of like and unlike terms.
For example: In the algebraic expression ‘8x +5y + 6z + 8 + 7x +2a’, 8x and 7x is like term because they have same variable i.e. x.
从 (3x 2 +4x–6) 中减去 (2x 2 –5x+7)。
解决方案：
Step to solve the problem:
Step 1: Write the given statement in the algebraic expression.
= (3x² +4x -6) – (2x² -5x +7)
Step 2: Open the bracket by using the distributive property of subtraction i.e. {(a+b)-(c-d) = a + b -c +d}
Multiplication of (-)ve with (-)ve, (+)ve with (+)ve is (+)ve, and multiplication of (-)ve with (+)ve is (-)ve.
= 3x² +4x -6 – 2x² +5x -7
Step 3: Find out the like terms and apply the arithmetic operation.
= 3x² -2x² +4x +5x -6 -7
= x² + 9x -13
So the subtraction of (2x²–5x+7) from (3x²+4x–6) is x² + 9x -13.
类似问题
问题 1：从 (15² -3x +2) 中减去 (9x² -6x +8)。
解决方案：
Write the given statement in the algebraic expression.
= (15x² – 3x + 2) – (9x² -6x +8)
Open the bracket and simply the terms by using the distributive property of the negative sign.
= 15x² – 3x + 2 – 9x² + 6x – 8
Find out the like terms and apply mathematics operation.
= 15x² – 9x² -3x +6x +2 -8
= 6x² +3x -6
So, the subtraction of (9x² -6x +8) from (15² -3x +2) is 6x² +3x -6.
问题 2：从 (x³ -9) 中减去 (8x³ – 6x² + 13x -6)。
解决方案：
Write the given statement in the algebraic expression.
= (x³ -9) – (8x³ – 6x² + 13x -6)
Open the bracket and simply the terms by using the distributive property of the negative sign.
= x³ – 9 – 8x³ +6x² -13x +6
Find out the like terms and apply mathematics operation.
= x³ – 8x³ +6x² -13x -9 +6
= -7x³ +6x² -13x -3
So, the subtraction of (8x³ – 6x² + 13x -6) from (x³ -9) is -7x³ +6x² -13x -3.