Adding Algebraic Expressions

Introduction to Adding algebraic expression:

Adding algebraic expression mean nothing but  combine the like terms  should not change the dislike terms. Expressions are a central concept in algebra .We can group the variables and constants to make algebraic expressions. A simple algebraic expressions like x + 3, y – 5, 4x + 5,10y – 5.Algeberic expression contains variables and constants. A variable can take various values. The value is not fixed. On the other hand, a constant has a fixed value. Examples of constants are: 4, 100, and 17


Example for Adding algebraic expression and concepts:


Example for algebraic expression:

Algebraic Expressions are obtained:

x^ 2, 2y^2,

1. Given algebraic expression x^ 2 is obtained by multiplying the variable x by itself;

x × x = x^ 2

Just as 4 × 4 is written as 42, we write x × x = x^ 2. It is commonly read as x squared

2. The expression 2y^2 is obtained from y: 2y^2 = 2 × y × y

Here by multiplying y with y we obtain y^2 and then we multiply y^2 by the constant 2

Example for adding algebraic expression:

Example 1: Adding algebraic:

2x^ 2+3x^ 2=5x^ 2 (add the like terms)

4xy+6xy+3y+4=10xy+3y+4 (arrange the terms and then add the like terms)

7xy-5xy+4z+6yz=2xy+4z+6yz

=2xy+2z(1+3y)(Taking common outside)

Basic concept Terms in algebraic expression

Terms of algebraic expression:

An algebraic function contains  two terms those are the like terms and dislike terms For example, in the expression 8xy – 5x + 6xy – 4,look at the terms 8xy and 6xy. The factors of 8xy are 8, x and y. The factors of 6xy are 6,x and y.
On the other hand the terms 8xy and –5x, have different algebraic factors.They are unlike terms. Similarly, the terms, 8xy and 4, are unlike terms. Also, the terms –5x and 4 are unlike terms. Understanding Variables and Expressions is always challenging for me but thanks to all math help websites to help me out.

Example problems in adding algebraic expression:


Steps in adding algebraic expression:

Procedure for adding algebraic function:

1.       Add 4x+4 +7y+5x+6

STEP 1: First we can add the co-efficient of x values (4x+5x) (like terms)=>9x

STEP 2: Second step we can add the  co-efficient of y values (7y)=>7y   (4x+7y is the unlike terms)

Step 3: Third step we can add the constant values (4+6)=10

STEP 4:  Adding the whole expression 9x+7y+10

Example problems in adding algebraic expression:

Example 1:

Adding the expression:   5xy+7xy+7z+6y-2xy+4yz

Solution:

5xy+7xy+7z+6y-2xy+4yz (given terms)

=5xy+7xy-2xy+6y+4yz+7z (arranging the like and dislike terms)

=12xy-2xy+6y+4yz+7z (Adding the like terms)

=10xy+6y+4yz+7z (perform the operation)

=10xy+2y(1+2z)+7z(Taking common terms)

Verbal Expressions into Algebraic Expressions

Variable expressions to algebraic expressions:

In Algebra an expression is a term which consists of both symbols and numbers. There are two types in that. They are Algebraic and Verbal expressions. Algebraic expression consists of signs and symbols. The signs involve signs of several operations like addition, subtraction, multiplication and division. The symbol involves all Arabic numerals and literal numbers. Ex: 3ax, 4yz…Verbal expression is the expression which consists of verbal phrases like sum, product, less than, etc…..

Verbal Expressions into Algebraic Expressions Explanation:

Some of the important operations that are used for this verbal expression into algebraic expression are,

Increased, Plus, more, total, add, sum                          +
Difference, Minus, less, decreased, subtract,               -
Product, Times, multiply, double, twice, product          *


In words they can be expressed as

Sum of a and b                                   a + b

Difference of a and b                         a – b

In addition with these basic operations some other operations like less than and greater than...

Less than                                         <
Greater than                                    >
Less than or equal                         <=
Greater than or equal                    >=

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Verbal Expressions into Algebraic Expressions Examples

1)      The sum of product of a number 2 and a  number x and the product of 6 and a number y

Sum represents the symbol + and the product represents the symbol *. in this question first consider the part “product of a number 2 and a number x” which can be represented as 2x and then the next part “product of 6 and a number y” which can be represented as 6y. Next is the final part of our expression which is “sum of product of a number 2 and a number x and the product of 6 and a number y” which completes our expression and so the algebraic expression is

2x + 6y

2)      8 greater than the variable y

The phrase greater than represent the symbol > and so this expression can be written as,

8 > y