Question

What is the expansion of `(x + 1)^4`?

Answer 1

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

Explanation:

According to Binomial Theorem expansion of `(x+a)^n` is

`x^n+nx^(n-1)a+(n(n-1))/(2!)x^(n-2)a^2+(n(n-1)(n-3))/(3!)x^(n-3)a^3+(n(n-1)(n-3)(n-4))/(4!)x^(n-4)a^4+.....+a^n`

Hence `(x+1)^4=x^4+4x^3xx1+(4xx3)/(2xx1)x^2xx1^2+(4xx3xx2)/(3xx2xx1)x xx1^3+(4xx3xx2xx1)/(4xx3xx2xx1)1^4`

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