Question

Expand ${\left(3m+2\right)}^5$using the Binomial Theorem.

Short answer

Thus,${\left(3m+2\right)}^5=243m^5+810m^4+1080m^3+720m^2+240m+32$

Step-by-step solution

Step 1. Given Information

The given polynomial is ${\left(3m+2\right)}^5$.

In the binomial Theorem, let role="math" localid="1646973173648" $a=3m,n=5$.

Step 2. Expand Polynomial

$$\begin{gathered} {\left(3m+2\right)}^5={}^{5}C_0{\left(3m\right)}^5{2}^0+{}^{5}C_1{\left(3m\right)}^4{2}^1+{}^{5}C_2{\left(3m\right)}^3{2}^2+{}^{5}C_3{\left(3m\right)}^2{2}^3+{}^{5}C_4\left(3m\right)2^4+{}^{5}C_5{2}^5 \\ {\left(3m+2\right)}^5=1\left(243m^5\right)+5\left(81m^4\right)2+10\left(27m^3\right)4+10\left(9m^2\right)8+5\left(3m\right)16+1\left(32\right) \\ {\left(3m+2\right)}^5=243m^5+810m^4+1080m^3+720m^2+240m+32 \end{gathered}$$