Simplifying Algebraic Expressions

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Algebraic expression are the expressions which can consist of different constant term (also called the numerical value), a variable term (usually denoted by alphabets like a, b, x, etc.) which are raised to an exponent or degree of various integers. There are various algebraic properties which help to simplify or evaluate given algebraic expressions.

Example 1: Simplify the algebraic expression, 3(x - 5) + 5(4x – 1) + x2 and evaluate its value when x = 2.

Solution: In order to simplify the above expression, we first use the Distributive Property and multiply the number to the braces.

(3x - 15) + (20 x – 5) + x2

Now combine the like terms

3x - 15 + 20 x – 5 + x2 = 23 x -20 + x2

To evaluate the simplified above expression, we plug in the place of ‘x’ as 2.

23 (2) -20 + (2)2

46 - 20 + 4 = 30

Hence the solution is 30
 
Example 2:Simplify the algebraic expression, 2(x - 5) + 4 (4x – 1) + x2 and evaluate its value when x = 1.

Solution: In order to simplify the above expression, we first use the Distributive Property and multiply the number to the braces.

(2x - 10) + (16 x – 4) + x2

Now combine the like terms

2x - 10 + 16 x – 4 + x2 = 18 x - 14 + x2

To evaluate the simplified above expression, we plug in the place of ‘x’ as 1.

18 (1) - 14 + (1)2

18 - 14 + 1 = 5

Hence the solution is 5
 

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