ab、a + b 和 b + ab 的总和是多少？
我们一直在处理不同的数字 1, 2, 3, 4 , ..... 等等，有四个基本运算符加法、减法、乘法和除法。我们将此分支称为“算术”。但是当我们使用字母来概括结果或表示未知数时，我们将其称为“代数”。使用字母和数字执行算术属性。这些字母代表未知数，我们称它们为“变量”。
Let take an example to better know algebra. Suppose we have to formalize an equation for finding the area of a rectangle. We know there is two unknown dimensions i.e. length and width. Let us assume the length of a rectangle is ‘l’ and width is ‘b’. Area of rectangle = Length × Width
By using the algebraic terms we can represent it as.
Area of Rectangle = l × b
代数表达式
代数表达式是数字和变量的组合。假设我们有数字和一个变量。我们可以通过使用不同的数字、变量和基本算术运算运算符来形成不同的方程。
例如，我们必须使用 x、+ 和 5 来形成代数方程。那么第一个表达式可以写成'x + 5'，再有一个方程可以写成'+5x'
在“x+5”中我们有两个术语，而在“+5x”中我们只有一个术语。基本上，算术运算运算符将项分开，根据项的数量，代数表达式可分为以下类型：
- 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：5x、6y 等
- 二项式：如果代数表达式中有两项，则称为二项式。示例：5x+3、9y + 7 等
- 三项式：如果代数项中的项数为三，则称为三项式。示例：5x+6y+9z、2x+6y+3 等。
- 多项式：如果代数表达式中的项数为一项或多于一项，则称为多项式。
Like terms and unlike terms:
If the variable part of two 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 equation 9x + 2y + 3 and 6x + 5y +6z, 9x and 6x is like terms, 2y and 5y is like terms because they have the same variable. Similarly 9x and 5y, 2y and 6z, etc are not like terms because they do not have the same variable.
代数表达式的加法：
对于两个代数项的相加，它们应该具有相同的项。如果它们没有相似的术语，则以相同的方式将它们与符号一起写出来。
示例： x 和 3x 可以添加为 4x，但 9x 和 3y 没有相同的项，因此将添加为 9x + 3y。
解决问题的步骤：
Step 1: Find the terms having like terms in the given algebraic expression.
Step 2: According to the arithmetic operators, do the calculation on the numerals part of the like term.
Step 3: By solving the like terms, reduce the algebraic term in the lowest term.
Step 4: Write the unlike terms along with the sign in the final answer.
ab、a+b、b+ab的和是多少？
解决方案：
Put the arithmetic operators of addition between the given three expressions.
= ab +(a+b) + (b+ab)
= ab +a +b +a + ab
Like term in the above expression is ab and a.
= ab + ab + a + a + b
Add the like terms.
= 2ab + 2a + b
So the sum of ab, a+b and b+ab is 2ab+2a+b .
类似问题
问题 1：xy、y+z 和 x+xy 之和是多少？
解决方案：
Put the addition arithmetic operator between the given three expressions.
= xy + (y + z) +( x + xy)
= xy + y + z + x + xy
Like term in the above expression is xy.
= xy + xy + x + y + z
Add the like terms.
= 2xy + x + y + z
So the sum of xy, y+z and x+xy is 2xy + x + y + z.
问题 2：x²y + 3y²、y² + z³和 z³ + xy 的总和是多少？
解决方案：
Put the addition arithmetic operator between the given three expressions.
= (x²y + 3y²) + (y² + z³) + (z³ + xy)
= x²y + 3y² + y² + z³ + z³ + xy
In the above expression, y² and z³ have like terms.
= 3y² + y² + z³ + z³ + x²y + xy
Add the like terms.
= 4y² + 2z³ + x²y + xy
So, the sum of x²y + 3y², y²+z³ and z³ + xy is 4y² + 2z³ + x²y + xy