Chapter 12, Problem 30RE

To determine

To expand: The expression using the binomial theorem.

Answer to Problem 30RE

The expansion of the expression ${(x+2)}^5$ using binomial theorem is $x^5+10x^4+40x^3+80x^2+80x+32$.

Explanation of Solution

Given information: ${(x+2)}^5$

${(x+2)}^5$

Let’s expand ${(x+2)}^5$ using binomial theorem,

  ${(x+2)}^5=c{}_0{x}^5+c{}_1{(x)}^4{(2)}^1+c{}_2{(x)}^3{(2)}^2+c{}_3{(x)}^2{(2)}^3+c{}_4{(x)}^1{(2)}^4+c{}_5{(2)}^5$

  $\text{ =}{x}^5+10x^4+40x^3+80x^2+80x+32$

Hence, The expansion of the expression ${(x+2)}^5$ using binomial theorem is $x^5+10x^4+40x^3+80x^2+80x+32$