Chapter 9.5, Problem 3QR

Solution

To calculate : the expanded product of $k\left(k+1\right)\left(k+2\right)$ .

The expanded product of $k\left(k+1\right)\left(k+2\right)$ is $k^3+3k^2+2k$ .

Given information :

The expression $k\left(k+1\right)\left(k+2\right)$ .

Formula used :

Multiply and then add the like terms.

Calculation :

Consider the expression $k\left(k+1\right)\left(k+2\right)$ ,

Expand the brackets.

  $\begin{array}{c}k\left(k+1\right)\left(k+2\right)=k\left(k\cdot k+k\cdot 2+1\cdot k+1\cdot 2\right)\\ =k\left(k^2+2k+k+2\right)\\ =k\cdot k^2+k\cdot 2k+k\cdot k+k\cdot 2\\ =k^3+2k^2+k^2+2k\end{array}$

Add the like terms.

  $k\left(k+1\right)\left(k+2\right)=k^3+3k^2+2k$

Thus, the expanded product of $k\left(k+1\right)\left(k+2\right)$ is $k^3+3k^2+2k$ .