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 $=4375$

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