SOLUTION: How do you: Find the coefficient of x^4 in the binomial expansion of (5+2x)^7 (with steps please)

Formula for a specific term in an expansion: (a + b)n = nCr-1(a)n-(r-1)(b)r-1, where r = term number 

(5 + 2x)7

Observing the binomial, it’s seen that the x-term, or “b” in the expansion of the binomial needs to be to the 4th power. 

Thus, the term that produces  is the term that needs to be determined. Thus, we can say that: , and that: 

4 = r – 1

4 + 1 = r

r, or term number = 5



Using the formula for a specific term in an expansion, term 5 or the 5th term can be determined, as follows: 

 (a + b)n = nCr-1(a)n-(r-1)(b)r-1, where r = term number 

(5 + 2x)7 = 7C5-1(5)7-(5-1)(2x)5-1, where r = 5th term 

(5 + 2x)7 = 7C4(5)7-4(2x)4

(5 + 2x)7 = 35(5)3(2x)4

(5 + 2x)7 = 4,375(16)x4

(5 + 2x)7 = 70,000x4

Thus, the  term, or 5th term of the binomial expansion: , is 70,000x4, which means

that the coefficient is 



Not to be confused, if the binomial's expressions were rearranged from  to ,

then  or  would be the 4th term.

You can do the check!! 

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