Question

Find the coefficient of x⁵ in (x+3)⁸

• A. 1512
• B. 1215
• C. 152
• D. 125

Answer 1

Answer:

A. 1512

$T_{r+1}=^nC_ra^{n-r}b^r$

n=8

a=x

b=3

$T_{r+1}=^8C_rx^{8-r}3^r$

$x^{8-r}=x^5$

$8-r=5$

$r=3$

$T_4=^8C_3 \times x^5 \times 3^3=\frac{8!}{3!\times5!}\times 3^3x^5$

$=\frac{8 \times 7 \times 6 \times 5!}{3! \times 5!} \times 3^3 x^5$

$=8 \times 7 \times 27x^5$

co efficient of x = 8 x 7 x 27 = 1512