# SIMPLIFYING EXPRESSIONS

"Simplifying Expressions" is the basic topic required for the students who would like to study Algebra in math.

## What is expression?

Expression is an algebraic or mathematical statement involves numbers,one or more variables and the operation symbols like +,-, x ,÷.

Simplifying expressions means combining all x terms as one x term and combining all constant terms as one constant term.

## Distributing and simplifying expressions

Distribution means sharing something among other recipients. In other words multiply the number or a variable which is outside the parenthesis with the inner terms.

Procedure of multiplying two polynomials  with exponents

We will multiply two or more polynomials in the following order.

(1) Symbol

(2) Number

(3) Variable

Let us see how it works

Multiply ( 5 x² ) and (-2 x³)

=  ( 5 x² )  x (-2 x³)

10 x

if we have only one x term then we have to put that x term as it is.

Problem 1:

Simplify the expression 7 (x - 3) + 2 (2x - 5) - 3(x - 5)

Solution:

7 (x - 3) + 2 (2x - 5) - 3(x - 5)

let us see how to simplify the given expression step by step

Step 1 :

Distributing the number which is outside the parenthesis with inner terms

=  7x - 21 + 4x - 10 - 3x + 15

Step 2 :

Combine the like terms

=  7x + 4x - 3x - 21 - 10 + 15

= 11x - 3x - 31 + 15

= 8x - 16

Problem 2:

Simplify the expression 4x - (2 + 4x) - 2 (x - 1) - 8 (x -3)

Solution:

=  4x - (2 + 4x) - 2 (x - 1) - 8 (x -3)

=  4x - 2 - 4x - 2x + 2 - 8x + 24

=  4x - 4x - 2x - 8x - 2 + 2 + 24

=  -10x + 24

## Simplifying expressions with fractions

Problem 3 :

Simplify the expression (2x - 7)/5 + (x + 9)/15 - (2x -2)/5

Solution :

=  (2 x - 7)/5 + (x + 9 )/15 - (2 x - 2 )/5

Now we are going to combine the like terms

Problem 4 :

Simplify the expression (3x+41)/2 + (x-3 )/5 -(9-2x)/6

Solution :

Now we are going to distribute the numbers which is out side the  parenthesis to the inner terms.Then combine the like terms

## Related topics

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WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6