Question

find the coefficient of xpower5in (x+3)power8

Answer 1

We know that General term of expansion (a + b)n is Tr+1 = nCr an–r br For general term of expansion(x + 3)8 Putting a = x , b = 3 , n = 8 Tr+1 = 8 Cr x8 – r 3r Now we need to find coefficient of x5 So x8 – r = x5 8 – r = 5 8 – 5 = r 3 = r r = 3 Putting r = 3 in (1) T3 + 1 = 8 C3 x8 – 3 33 = 8!/(3! 5!) x5 × (3 × 3 × 3) = (8 × 7 × 6 × 5!)/(3! × 5!) × x5 × (3 × 3 × 3) = (8 × 7 × 6 ×3 × 3 × 3)/(3 × 2) x5 = 1512 x5 Hence coefficient of x5 = 1512