Analysis and Approaches for IBDP Maths Ebook 2 | Page 56

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(b)
x 1 3
� �
(1 � x)(3 � x) 4(1 � x) 4(3 � x)
x 1 �1
3 � 1 �
� (1 � x) � �1�
x�
(1 �x)(3 �x) 4 12 � 3 �
x
(1 �x)(3 �x)
1 �
( �1)( �2)
�
4 �
2!
2
� 1 � ( �1)( �x) � ( �x)
�
2
1 � � 1 � ( �1)( �2) � 1 �
� 1 � ( �1)
x � x �
4 � � � � �
� � 3 � 2! � 3 �
x
� � � �
(1 �x)(3 �x) 4
1 � 1 1
�
4 � 3 9
2
� 1� x� x �
1 (1
2
x x )
�
�
�
�1
x 1 1 1 1 1 1
x x x x
(1 � )(3 � ) 4 4 4 4 12 36
2 2
x x � � � � � � �
x 1 2
x x
(1 � )(3 � ) 3 9
2
x x � � �
Thus, the coefficient of
2
x is 2 9 .
�
�
�
�
�
�
M1A1
A1
A1
[4]
Exercise 16
2
1. (a) Express
in partial fractions.
(2 �x)(5 �x)
(b)
[4]
Hence, by using the extended binomial expansion, find the sum of the coefficient
2
2
of x and the coefficient of x of the expansion of
.
(2 �x)(5 �x)
1�
x
2. (a) Express
2
(4 � x)
(b)
in partial fractions.
Hence, by using the extended binomial expansion, find the coefficient of
1�
x
expansion of .
2
(4 � x)
[4]
[4]
3
x of the
[5]
46
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