Algebraic Expressions Definition
The algebraic expressions have the variables and the constants. The algebraic
expressions are the finite combination of the symbols that are formed according to the
rules of the context.
The algebra is an expression which is used to designate the value for the given values
in the expression. The expression might be depending on the values assigned to the
values assigned in the expression.
The expression is the syntactic concept in the algebra. The online provides the
connectivity between the tutors and the students. This article has the information about
learn online algebraic expressions.

Simplifying Algebraic Expressions
Below are the examples on Simplifying algebraic expressions


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Example 1
Compute the factors for the expression x2+ 56x+ 768.
Solution:
The given expression is x2+ 56x+ 768.
Step 1: x2+ 56x+ 768 = x2+24x+ 32x+ (24x 32)
Step 2: x2+ 56x+ 768 = x(x+24) + 32(x +24)
Step 3: x2+ 56x+ 768 = (x+24) (x+32)
Step 4: x+24 and x+32
The factors for the given expression x2+ 56x+ 768 are (x +24) and (x +32).
Example 2
Compute the factors for the expression x2+ 76x+ 1440.
Solution:
The given expression is x2+ 76x+ 1440.
Step 1: x2+ 76x+ 1440 = x2+36x+ 40x+ (36x 40)


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Step 2: x2+ 76x+ 1440 = x(x+36) + 40(x +36)
Step 3: x2+ 76x+ 1440 = (x+36) (x+40)
Step 4: x+36 and x+40
The factors for the given expression x2+ 76x+ 1440 are (x +36) and (x +40).
Example 3
Simplify the expression 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y.
Solution:
The given expression is 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y.
Step 1: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = x y (24 +14 +10) + x2y (10+ 16)
Step 2: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = 48 x y + x2y (10+ 16)
Step 3: 24xy + 10 x2y + 14 x y + 16 x2y + 10 x y = 48 x y + 26 x2y
The value for the given expression 12xy + 13 x2y + 16 x y + 20 x2y is 48 x y + 26 x2y

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Solving Linear Equations with Fractions
Learn about solving linear equations with fraction. In a linear equation the degree of
the equation wil be always one. It contains variables and constants and contain a first
power of variables, also does not contain product of two variables.
A linear equation may contain one or more variables in it. Linear equation is a simple
equation. It has lots of application in mathematics and many other fields. Solving a
equation is finding the value of unknown variables in the equation. The equation
involving fraction contains terms of the form a/b.
Here the method to solve is by taking the fraction term to one side and taking least
common multiple(LCM) and them cross multiply the equations bring terms with
variables to one side and constants to other side.
Take variable common and then take remaining term to other side and simplify
them.Now we wil see some examples of solving equations with fraction below.



Solving Equations with Fractions

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Below are the examples on solving linear equations with fractions -
Example 1:
Solve the linear equation y/4 = 3
Solution:
Step 1: Given equation
y/4 = 3
Step 2: Multiply by 4 on both sides
y/4 x 4 = 3 x 4
y = 12
Example 2:
Solve the linear equation x/3 + 5 = 9
Solution:
Ste p 1: Given equation

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x/3 + 5 = 9
Step 2: Subtract 5 on both sides of the equation
x/3 + 5 - 5 = 9 - 5
x/3 = 4
Step 3: Multiply by 3 on both sides of the equation
x/3 x 3 = 4 x 3
x = 12
Example 3:
Solve the linear equation x/3 + (5x)/3 = 4
Solution:
Step 1: Given equation
x/3 + (5x)/3 = 4
Ste p 2: Add the fractions x/3 and (5x)/3

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Since the denominators of both the fractions are common, we can add the numerators
directly as fol ows.
(x + 5x)/3 = 4
(6x)/3 = 4
Step 3: Multiply by 3 on both sides of the equation
6x = 12
Step 4: Divide by 6 on both sides
x = 2
Example 4:
Solve the linear equation m/3 + (3m)/5 - 4= 6
Solution:
Step 1: Given equation
m/3 + (3m)/5 - 4 = 6


Step 2: Add 4 on both sides of the equation

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