7th Class Mathematics Algebraic Expressions Operations on Algebraic Expression

Operations on Algebraic Expression

Category : 7th Class

*     Operations on Algebraic Expression

 

Addition and subtraction of an algebraic expressions mean addition and subtraction of like terms.                

 

*      Addition of an Algebraic Expression

For addition of algebraic expression we may follow any one of the following methods:                                

 

Row Method

In this method, write all expression in a single row then arrange the terms to collect all like terms together and add it.                                

 

Column Method

In this method, arrange each expression in such a way that each like term is placed one below to other in a column.  

 

 

Add \[3x+2y+3z\]and \[2x-3y+4z\]

Solution:                

\[(3x+2y+3z)+(2x-3y+4z)\]         

\[=(3x+2x)+(2y-3y)+(3z+4z)=5x-y+7z\] 

Column method                

\[3x+2y+3z\]                

\[\frac{+2x-3y+4z}{5x-y+7z}\]                

 

*      Subtraction of an Algebraic Expression

For subtraction also you may follow any one of the following method                                

 

Row Method

We arrange algebraic expression in a row and change the sign (from + to ?, ? or ? to +) of all terms which is to be subtracted. The two expression then added as above.                                

 

Column Method

Arrange two expression in such a way that like terms are placed one below the other and change the sign (from + to ?,or ? to +) of algebraic expression which is to be subtracted.  

 

 

Subtract  \[5{{a}^{2}}{{b}^{2}}+6{{a}^{2}}{{b}^{2}}+4\] from \[7{{a}^{2}}b-6{{a}^{2}}{{b}^{2}}+5\]                                

Solution:                

By row method,                

\[(7{{a}^{2}}b-6{{a}^{2}}{{b}^{2}}+5)-(5{{a}^{2}}b-6{{a}^{2}}{{b}^{2}}+4)\]                

\[=7{{a}^{2}}b-6{{a}^{2}}{{b}^{2}}+5-5{{a}^{2}}b-6{{a}^{2}}{{b}^{2}}-4\]

Arrange like terms and add, we get \[=2{{a}^{2}}b-12{{a}^{2}}{{b}^{2}}+1\]

By column method,

\[7{{a}^{2}}b-6{{a}^{2}}{{b}^{2}}+5\] \[\frac{{{\underline{5a}}^{2}}b+6\underline{{{a}^{2}}}{{b}^{2}}+\underline{4}}{2{{a}^{2}}b-12{{a}^{2}}{{b}^{2}}+1}\]  



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