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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