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Find the coefficient of a4 in the expansion of the product (1 + 2a)4 (2 - a)5 .

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+2 votes
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Best answer

(1 + 2a)4 

= 1 + 4​​​​​​C1.2a + 4​​​​​​C2.(2a)2 + 4​​​​​​C3.(2a)3 + (2a)4

= 1 + 8a + 24a2 + 32a3 + 16a4                        ..... (1)

Again, 

(2 - a)5

= 25 - ​​​​​​5C1​​​​​​.24.a + 5​​​​​​C2.23.a2 - 5C3.22.a3 + 5​​​​​​C4.2.a​​​​​4 - ​​​​​​a5

=32 - 80a + 80a2 - 40a3 +10a​​​​4 - a5 

Now, 

(1 + 2a)4 (2 - a)5

= [1 + 8a + 24a2 + 32a+ 16a4].[32 - 80a + 80a2 - 40a+ 10a​​​​​​4 - a5]

Required coefficient of a4 in the product 

= 1 × 10 + 8 × (-40) + 24 × 80 + 32 × (-80) + 16 × 32

= -438

by (23.9k points)
+2
This is more simplified.
+2 votes
by (42.0k points)

We know that

by (23.9k points)
+2
Your merhod of solving this  question is very lengthy.

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