What is the expansion of ${(x + 1)}^{4}$ $(x + 1)^4$ ?

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Answer 1 · 2016-09-24T15:57:33

${(x + 1)}^{4} = x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1$ $(x+1)^4=x^4+4x^3+6x^2+4x+1$

According to Binomial Theorem expansion of ${(x + a)}^{n}$ $(x+a)^n$ 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 $(x+1)^4=x^4+4x^3xx1+(4xx3)/(2xx1)x^2xx1^2+(4xx3xx2)/(3xx2xx1)x xx1^3+(4xx3xx2xx1)/(4xx3xx2xx1)1^4$

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

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