Question

Find the number of terms in the expansion of the following.
$(1+3x+3x^2+x^3{)}^5$.

Answer 1

$(1+3x+3x^2+x^3{)}^5$

$(x^3+3x^2+3x+1{)}^5$

$(x^3+3x^2(1)+3x(1{)}^2+(1{)}^3{)}^5$

$\left[\right(x+1{)}^3=x^3+1+3x^2+3x]$

$\left[\right(a+b{)}^3=a^3+b^3+3a^{2}b+3a{b}^2]$

$\left(\right(x+1{)}^3{)}^5$

$(x+1{)}^{15}$

A binomial expansion with power n has (n+1) terms.

Here the number of terms in the expansion of $(1+3x+3x^2+x^3{)}^5=16$