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Exercise 8.2 

Find the coefficient of  

Q1.  x⁵ in (x + 3)⁸

Solution:

(x + 3)⁸

General term ⁿC_r a^n-r b^r

 n = 8, then

⁸C_r x^8-r 3^r ⇒ x⁵ = x^8-r

5 = 8-r

∴ r = 8-5 = 3

⁸C₃ x^8-3 3³ = ⁸C₃ x⁵ 3³

Coefficient in x⁵ = ⁸C₃ 3³

= 1512 

Q2.  a⁵b⁷ in (a-2b)¹²

Solution:

 (a-2b)¹²

General Term T_r+1 = ⁿC_r a^n-r b^r

¹²C_r a^12-r b^r

∴12 – r = 5 ⇒ r = 12 – 5 = 7

 a⁵b⁷ is 8 term

T₈ = ¹²C₇ a⁵ b⁷

     = ¹²C₇ a⁵ (-2b)⁷

​

    = - 72 × 11 × 2⁷

    = - 72 × 11 × 128 = - 101376 

Write the general term in the expansion of

Q3. (x² - y)⁶

Solution:

General term of (x² - y)⁶

n = 6, a = x², b = (-y) 

General Term T_{r +1} = ⁿC_r a^n-r b^r

=  6Cr (x2)6-r (-y)r

= 

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