How do you find the coefficient of x^5 in the expansion of (2x+3)(x+1)^8?

1 Answer
George C.
Jul 12, 2015

Calculate the coefficients of x^5x5 and x^4x4 in (x+1)^8(x+1)8, then multiply by 33 and 22 then add to get the answer 308308

Explanation:

(x+1)^8 = sum_(n=0)^(n=8) ((8),(n))x^n

The coefficient of x^4 in (x+1)^8 is ((8),(4)) = (8!)/(4!4!) = 70

The coefficient of x^5 in (x+1)^8 is ((8),(5)) = (8!)/(5!3!) = 56

So the coefficient of x^5 in (2x+3)(x+1)^8 is

2*70 + 3*56 = 140 + 168 = 308

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