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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.

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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.