Algebraic Expressions

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Algebraic expression is an expression which contains variables and constants. In algebraic expressions we can perform all the algebraic operations like subtraction, addition, division, multiplication, we can also find the root and exponent in those expressions. There are different types of algebraic expressions that may contain one variable or more than that. The algebraic expressions can be simplified or solved by using different algebraic operations.

The terms like 2x, 2x^3 + 4, 8x^2 – 9x + 7, 5a^2 + 8b – 10c are all the examples of algebraic expressions.  

Following are some examples to understand the concept better.

Example 1: Simplify given polynomial expressions (2x^2 + 3x – 4) + (4x^2 + 7x + 8).

Solution: In order to solve these types of problems, first we open parenthesis sign

 2x^2 + 3x – 4 + 4x^2 + 7x + 8

Now writing the like terms together, we get

2x^2 + 4x^2 + 3x + 7x – 4 + 8

Simplifying the like terms, we get

6x^2 + 10x + 4

Example 2: Simplify algebraic expressions (x – 2) (x + 2) + 2x^2 + 4x – 8 – (2x^2 + 3x – 7)

Solution: Given expressions (x – 2) (x + 2) + 2x ^2 + 4x – 8 – (2x ^2 + 3x – 7)

Following the PEMDAS rule, the parenthesis should be opened first

x^2 – 4 + 2x^2 + 4x – 8 – 2x^2 – 3x + 7

Writing the like terms together, we get

x^2 + 2x^2 + 4x – 3x + 7 – 4

Simplifying the like terms, we get

3x^2 + x + 3
 

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