# 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

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