Question

Coefficient of x^4 in (2x-1)^5

Answer 1

`-80`

Explanation:

Use binomial expansion formula:

`(a+b)^n=a^n+C^n_1a^(n-1)b^1+C_2^na^(n-2)b^2+...+b^n`

In your case,

`(2x-1)^5=\\ \\=(2x)^5+C^5_1(2x)^4(-1)^1+C^5_2(2x)^3(-1)^2+C^5_3(2x)^2(-1)^3+C^5_4(2x)^1(-1)^4+(-1)^5`

Find the term containing
`x^4`:

`C^5_1(2x)^4(-1)^1=(5!)/(1!(5-1)!)\cdot 16x^4\cdot (-1)=-5\cdot 16x^4=-80x^4`