Question

find the coeffiect of x^5 in expansion of (x+3)^8

Answer 1

We have,
(x + 3)⁸

Now,

Tᵣ₊₁ = ⁸Cᵣ (x)⁸⁻ʳ (3)ʳ ..........(i)

To find the coefficient of x⁵,

x⁸⁻ʳ = x⁵

Or 8-r = 5

Or x = 3

Thus, putting the value of x = 3 in (i), we get,

T₃₊₁ = ⁸C ₃ (x)⁸⁻³ (3)³

Or 8 × 7 × 6/ 3 × 2 × 1 (x⁵) × 27

Or 56 × 27 x⁵

Or 1512 x⁵

Thus, the coefficient of x⁵ is 1512 in the expansion (x + 3)⁸