Question

What is the coefficient of x^4 in expansion of (2x+1)^4 ?

Answer 1

Consider the typical binomial expansion: (1 + x)ⁿ


`(1 + x)^(n) = \sum_(r=0)^(n) \left(\begin{array}{ccc}n\\r\end{array}\right)(1)^(n - r)(x)^(r)`


`\therefore (1 + 2x)^(4) = \sum_(r=0)^(4) \left(\begin{array}{ccc}4\\r\end{array}\right)(1)^(4 - r)(2x)^(r)`

Since we need to find the coefficient of x⁴, then we need to let r = 4 in order to find the coefficient.

Thus, the coefficient is:

`\left(\begin{array}{ccc}4\\4\end{array}\right)(1)^(4 - 4)(2x)^(4)`

`= 16x^(4)`

Thus, the coefficient of x⁴ is 16.

Answer 2

The expansion would be 16x^4+32x^3+24x^2+8x+1
The coefficient would be 16

Hope I didn't mess up for your sake