NCERT Class XI Mathematics - Binomial Theorem - Solutions
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Question : 36
Total: 36
Find the expansion of ( 3 x 2 – 2 a x + 3 a 2 ) 3
Solution:
Let 3 x 2
Then[ 3 x 2 − 2 a x + 3 a 2 ] 3 [ y + 3 a 2 ] 3
=
C 0 y 3 +
C 1 y 2 ( 3 a 2 ) +
C 2 y ( 3 a 2 ) 2 +
C 3 ( 3 a 2 ) 3
= ( 3 x 2 − a x ) 3 + 3 ( 3 x 2 − 2 a x ) 2 ( 3 a 2 ) + 3 ( 3 x 2 − 2 a x ) ( 9 a 4 ) + ( 27 a 6 )
= [
C 0 ( 3 x 2 ) 3 +
C 1 ( 3 x 2 ) 2 ( − 2 a x ) +
C 2 ( 3 x 2 ) ( − 2 a x ) 2 +
C 3 ( − 2 a x ) 3 ] 3 [
C 0 ( 3 x 2 ) 2 +
C 1 ( 3 x 2 ) ( − 2 a x ) +
C 2 ( − 2 a x ) 2 ] ( 3 a 2 ) + 3 ( 27 x 2 a 4 − 18 a 5 x ) + 27 a 6
=27 x 6 − 54 a x 5 + 36 a 2 x 4 8 a 3 x 3 + 81 a 2 x 4 108 a 3 x 3 + 36 a 4 x 2 + 81 a 4 x 2 54 a 5 x + 27 a 6
=27 x 6 − 64 a x 5 + 117 a 2 x 4 116 a 3 x 3 117 a 4 x 2 − 54 a 5 x + 27 a 6
Then
=
=
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