What is the coefficient of #a^3b^4# in the expansion of #(5a + b)^7#?

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Answer 1 · 2017-12-07T20:21:15

coefficient #=4375#

the binomial expansion formula is:

#(a+b)^n=sum_(r=0)^n color(white)(1)^n C_ra^(n-r)b^r#

we have

#(5a+b)^7#

we just want the #" "a^3b^4" "#term

so

#n=7#

giving the term

# color(white)(1)^7 C_4(5a)^3b^4#

#=35xx125a^3b^4#

coefficient #=4375#