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Title: 6. Algebra Multiplication of Algebraic Expressions Part 006
Description: This file contains sample problems and step-by-step explanatory solutions for multiplying algebraic expressions.
Description: This file contains sample problems and step-by-step explanatory solutions for multiplying algebraic expressions.
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04 - 20 - 23
ALGEBRA:
Multiplication
of
Algebraic
Expressions (Sample Problems & Solutions) Part 006
1
...
Solution:
Multiplying the two expressions, we have,
3 2�2 − 1
2�2 + � − 3
Distribute the second term into the first term or vice versa,
we have,
� ���
� ��� − �
��� + � − �
��� + � − � − � ��� + � − �
Simplifying further thru distributive property, we have,
� ��� ��� + � − � − 1 2�2 + � − 3
��� + � ��� − � ��� − 1 2�2 + � − 3
6�4 + 3 2�3 − 3 6�2 − � ��� + � − �
6�4 + 3 2�3 − 3 6�2 − ��� − � + �
6�4 + 3 2�3 − � ��� − ��� − � + 3
6�4 + 3 2�3 − � � + � �� − � + 3
Therefore, the product of the two expressions is ��� + � ��� −
� � + � �� − � + �
...
Multiply the following: 0
...
1� + 1 6
...
2
...
6�4 − 3
...
7� − 4
...
�
�
...
� − 3
...
7� − 4
...
7� − 4
...
���� − 3
...
7� − 4
...
7� − 4
...
02�5 − 2
...
� + 1 6
...
2
4
...
52�4 − ��
...
7� − 4
...
02�5 − 2
...
77�2 + 13
...
�
4
...
52�4 − 20
...
02� + �
...
02�5 − 2
...
77�2 + ��
...
2
4
...
52�4 − 20
...
��� − 4
...
3
...
First, distribute the second expression to the first expression
or vice versa, we have,
1 2 8
1
� − �+
4
3
2
3 1 2 8
1
� � − �+ −1
2 4
3
2
3
�−1
2
1 2 8
1
� − �+
4
3
2
Applying the distributive property, we have,
� � � �
�
1
8
1
� � − �+
− 1 �2 − � +
� �
�
�
4
3
2
� �
�
1
8
1
� − ��� + � − 1 �2 − � +
�
�
4
3
2
3 3
3
�
�
�
� − 4�2 + � − � �� − � +
8
4
�
�
�
3 3
3
�
�
�
� − 4�2 + � − �� + � −
8
4
�
�
�
Simplifying further, we have the following,
3 3
3
�
8
1
� − ��� + � − �� + � −
8
4
�
3
2
3 3 �� � 3
8
1
� −
� + �+ �−
8
�
4
3
2
3 3 17 2 �
�
1
� − � + �+ �−
8
4
�
�
2
3 3 17 2 ��
1
� − � +
�−
8
4
��
2
Therefore, the product of the given problem is
�
�
...
Simplify the following:
Solution:
1
2− �
4
1
2− �
4
�2 − 2� +
�2 − 2� +
3
2
...
5
...
3 2
4
First, distribute the first expression to the second expression
or vice versa, we have,
� �
�
�
� � �
� �
�� +
� −
�
�
�
� �
� �
�
�� +
�� +
−
�
�
�
Applying the distributive property, we have the following,
� �
3 2
� �
3
�
�� +
−
2y +
�
4
�
2
� � � � � 3
3 2
2y +
� +
� −
�
��
2
4
2 4 3 2 3 �
� �
�� +
y +
y −
4
16
�
�
2 4 3 2 3 � �
� �
y +
y −
�−
4
16
�
�
Therefore, the result on simplifying the problem is
� �
�
�−
� �
�
Title: 6. Algebra Multiplication of Algebraic Expressions Part 006
Description: This file contains sample problems and step-by-step explanatory solutions for multiplying algebraic expressions.
Description: This file contains sample problems and step-by-step explanatory solutions for multiplying algebraic expressions.