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04 - 19 - 23

ALGEBRA:
Multiplication
of
Algebraic
Expressions (Sample Problems & Solutions) Part 005
1
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Solution:

Multiplying the two expressions, we have,
� + 1 �2 − 1

Distribute the second term into the first term or vice versa,
we have,
� + � �� − �
� �� − � + � �� − �

Simplifying further thru distributive property, we have,
� �� − � + 1 �2 − 1
�� − � + 1 �2 − 1
�3 − � + � �� − �
�3 − � + �� − �
�� + �� − � − �

Therefore, the product of the two expressions is �� + �� − � − �
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Simplify the following: �2 � + 1 � − 1
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3
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Solution:

�2 + � − 1 �2 + 1

First, distribute the second expression to the first expression
or vice versa, we have,
�� + � − � �� + �
�� �� + � + � �� + � − � �� + �

Applying the distributive property, we have,
�� + �� + �� + � − �� − �

Simplifying further, we have the following,
�4 + �� + �3 + � − �� − 1
�4 + 0 + �3 + � − 1

Therefore, the product of the given problem is �� +�� + � − �
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Simplify the following: �3 − �2 + 1 − �3 + 3�2 − 1
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5
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Solution:

y y4 − 1 y2 + 3 − 2y

First, distribute the first expression to the second expression
or vice versa, we have,
� �� − � y2 + 3 − 2y
�� − � y2 + 3 − 2y

Again, distribute the first expression to the second
expression or vice versa, we have,
�� − � �� + � − ��
�� �� + � − �� − � �� + � − ��

Applying the distributive property, we have the following,
�� + ��� − ��� − �� − �� + ���

With further simplification, we have,

�� + ��� − ��� − �� − �� + ���
�� − ��� + ��� − �� + ��� − ��

Therefore, the result on simplifying the problem is �� − ��� +
��� − �� + ��� − ��

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