Question

Find the coefficient of x^7 in the expansion of (3x+4)^11

Answer 1

Use the binomial theorem:

`(a+b)^n=\displaystyle\sum_(k=0)^n\binom nka^(n-k)b^k`

In this case,

`(3x+4)^(11)=\displaystyle\sum_(k=0)^(11)\binom{11}k(3x)^(11-k)4^k`

The
`x^7` term occurs for
`k=4`:

`\dbinom{11}4(3x)^(11-4)4^4=(11!)/(4!(11-4)!)3^74^4x^7=184,757,760x^7`