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04 - 16 - 23

ALGEBRA: Addition of Algebraic Expressions
(Sample Problems & Solutions) - Part 001
1
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Solution:

Add up all the five algebraic expressions as follows,
�2 + � + 1 + 3�2 + 4 + 5� − 4 + �2 − 2� + 3

Remove all parenthesis for simplifying the expressions as
follows,
�2 + � + 1 + 3�2 + 4 + 5� − 4 + �2 − 2� + 3

Now, indicate all expressions with �2 and add them as
follows,
�� + � + 1 + ��� + 4 + 5� − 4 + �� − 2� + 3
��� + � + 1 + 4 + 5� − 4 − 2� + 3

Then, for the expression with � ,

5�2 + � + 1 + 4 + �� − 4 − �� + 3
5�2 + �� + 1 + 4 − 4 + 3

Lastly, for the last term,

5�2 + 4� + � + � − � + �
5�2 + 4� + �

Therefore, the sum of the give algebraic expressions is ��� +
�� + �
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Find the sum: �2 + 10� + 1 , and 3�2 − 6� + 1
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3
...

Solution:

Add up all the three algebraic expressions as follows,
−7�2 + 4� − 1 + −�2 − 1 + 6�2 + 4�

Simplifying the expressions, as follows,

−7�2 + 4� − 1−�2 − 1 + 6�2 + 4�

Then, indicate the expressions with similar variables and add
them all as follows,
−��� + 4� − 1−�� − 1 + ��� + 4�
−��� + 4� − 1 − 1 + 4�
−2�2 + �� − 1 − 1 + ��
−2�2 + �� − 1 − 1
−2�2 + 8� − � − �
−2�2 + 8� − �

Therefore, the sum of the given algebraic expressions is −��� +
�� − �
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Find the sum of the following expressions: 6� − 4�2 ,
1 + � , and 8�2 − 1
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5
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8� − 4 ,

Solution:

Add up all the given algebraic expressions as follows,
8� − 4 + 7�2 + � + 3�2 + 4 − �

Then, indicate the expressions with similar variables and add
them all as follows,
8� − 4 + ��� + � + ��� + 4 − �
���� + 8� − 4 + � + 4 − �
10�2 + �� − 4 + � + 4 − �
10�2 + �� − 4 + 4
10�2 + 8� − � + �
10�2 + 8� + �

Therefore, the sum of the given algebraic expressions is ���� +
��

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