Find the coefficient of

x⁵ in (x + 3)⁸

The general term T_r+1 in the binomial expansion is given by T_r+1 = ⁿC_r a^n-r b^r

Here x⁵ is the T_r+1 term so

a= x, b = 3 and n =8

T_r+1 = ⁸C_r x^8-r 3^r……………1

For finding out x⁵

We equate x⁵= x^8-r

⇒ r= 3

Putting value of r in 1 we get

T₃₊₁ = ⁸C₃ x^8-3 3³

= 1512 x⁵

Hence the coefficient of x⁵= 1512