## Intermediate Algebra for College Students (7th Edition)

$x^3+6x^2+12x+8$
According to the Binomial Theorem or Binomial expansion, the expansion for $(x+y)$ in the any number of power can be calculated as: $(x+y)^n=\displaystyle \binom{n}{0}x^ny^0+\displaystyle \binom{n}{1}x^{n-1}y^1+........+\displaystyle \binom{n}{n}x^0y^n$ Let's see how this formula works: $(x+2)^3=\displaystyle \binom{3}{0}x^32^0+\displaystyle \binom{3}{1}x^{2}2^1+\displaystyle \binom{3}{2}x^12^2+\displaystyle \binom{3}{3}x^02^3$ or, $=x^3+3(x^2)2+12x+8x^0$ or, $=x^3+6x^2+12x+8$