Question

How do I find the binomial expansion of `(2x+1)^4`?

Answer 1

Note that the notation for the binomial coefficients is incorrect . It should not look like a fraction. The fraction bar should be removed the numbers should be on top of each other vertically.

`=(4/0)(2x)^4(2)^0+(4/1)(2x)^3(2)^1+(4/2)(2x)^2(2)^2+(4/3)(2x)^1(2)^3+(4/4)(2x)^0(2)^4`

`=(1)(2x)^4+(4)(2x)^3(2)+(6)(2x)^2(2)^2+(4)(2x)(2)^3+(1)(2)^4`

`=(2x)^4+(4)(2x)^3(2)+(6)(2x)^2(2)^2+(4)(2x)(2)^3+(2)^4`

`=16x^4+64x^3+48x^2+64x+16`