Find the coefficient of
(i)x5 in the expansion of (x + 3)8
(ii) x6 in the expansion of .
(iii) x-15 in the expansion of .
(iv) a7b5 in the expansion of (a – 2b)12.
(i) Here, a=x, b=3 and n=8
We have a formula,
To get coefficient of x5 we must have,
(x)8-r = x5
• 8 - r = 5
• r = 3
Therefore, coefficient of x5
= 1512
(ii) Here, a=3x2, and n=9
We have a formula,
To get coefficient of x6 we must have,
(x)18-3r = x6
• 18 - 3r = 6
• 3r = 12
• r = 4
Therefore, coefficient of x6
= 126×3
= 378
(iii) Here, a=3x2, and n=10
We have a formula,
To get coefficient of x-15 we must have,
(x)20-5r = x-15
• 20 - 5r = -15
• 5r = 35
• r = 7
Therefore, coefficient of x-15
But ……….
Therefore, qthe coefficient of x-15
(iv) Here, a=a, b=-2b and n=12
We have formula,
To get coefficient of a7b5 we must have,
(a)12-r (b)r = a7b5
• r = 5
Therefore, coefficient of a7b5
= 792. (-32)
= -25344