求解 (4a ² – 2a +15) + (a ² + 3a – 11)

代数是处理数字和变量研究的数学分支。它有助于表示数学表达式中的条件或问题。大多数数学分支，如微积分、坐标几何等都使用代数。它使用 p、q、r、s 等变量以及除法、减法、乘法和加法等运算来创建表达式。例如，4x + 2y = 10。这里，a和y是变量，+代表加法运算。

代数表达式

代数表达式由各个部分、常数、变量和数学运算组成。它可以使用各种数学运算组合在一起，例如加法（+）、减法（-）、乘法（x）和除法（/）。它也被称为数学陈述。

代数表达式的加法

When adding the algebraic expressions we have to gather all the like terms and add them together. Or we can say that the sum of the many like terms will be the like term whose coefficient is the total of the coefficients of the like terms.

求解代数表达式的步骤

第 1 步：括号与符号的评估一起打开。

步骤 2：将包含相同变量幂的项收集在一起。

第 3 步：求解相似项以实现每个变量的奇异项。

第四步：得到简化结果作为最终答案。

求解 (4a ² – 2a +15) + (a ² + 3a – 11)

解决方案：

We have, 

(4a² – 2a + 15) + (a² – 3a – 11)

Open the brackets

4a² – 2a + 15 + a² – 3a – 11

Take all the like terms together as follows

4a² + a² – 2a – 3a + 15 – 11

Now calculating the values,

5a² + 5a + 4 

Therefore, this equation can be simplified to obtain the following answer. 

示例问题

问题 1. 化简 6(4x – 2) + x((3x)/ (3)) + 16 – 5x

解决方案：

Here we have 6(4x – 2) + x((3x)/ (3)) + 16 – 5x

First open brackets

⇒ 24x – 12 + 3x²/3 + 16 – 5x

simplifying

⇒ 24x – 12 + x² + 16 – 5x

Now taking the like terms together

⇒ x² + 24x – 5x – 12 + 16 

Now simplify the like terms

⇒ x² + 19x + 4 

问题 2. 简化 2x (8 – 2x) – 2x (6 – 2x)

解决方案：

Here we have to simplify 2x (8 – 2x) – 2x (6 – 2x)

First open the brackets

⇒ 16x – 4x² – 12x + 4x²

Now combine the like terms

⇒ -4x² + 4x² + 16x – 12x

Further simplifying the like terms

⇒ 4x

问题 3. 简化 4st + 6t – 2s + 10t + 8s

解决方案：

Here we have to simplify 4st + 6t – 2s + 10t + 8s

Take the like terms together

⇒ 4st + 6t + 10t – 2s + 8s

Now do the addition and subtraction of the like terms

⇒ 4st + 16t + 6s

Therefore,

Simplification of 4st + 6t – 2s + 10t + 8s is 4st + 16t + 6s

问题 4. 简化 x(2x + 3y – 4) – x ² + 4xy – 12x？

解决方案：

Here we have to simplify  x(2x + 3y – 4) – x ² + 4xy – 12x

First open the brackets

⇒ 2x² + 3xy – 4x – x² + 4xy – 12x

Now take all the like terms together

⇒ 2x² – x² + 3xy + 4xy – 4x – 12x

Now solving the like terms

⇒ x² + 7xy – 16x