Chapter 4.3, Problem 32WE

To determine

To calculate: The multiplication of the term $\left(y^2-2y+1\right)\left(y^2+y+1\right)$ .

Answer to Problem 32WE

The required multiplication is $y^4-y^3-y+1$ .

Explanation of Solution

Given information:

The algebraic term is $\left(y^2-2y+1\right)\left(y^2+y+1\right)$ .

Formula Used:

Distribution property is

  $\begin{array}{c}\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)\\ =ac+ad+bc+bd\end{array}$

Calculation:

Consider the given algebraic term $\left(y^2-2y+1\right)\left(y^2+y+1\right)$ .

Now multiply. Use the distribution property.

  $\begin{array}{c}\left(y^2-2y+1\right)\left(y^2+y+1\right)=y^2\left(y^2+y+1\right)-2y\left(y^2+y+1\right)+\left(y^2+y+1\right)\\ =y^4+y^3+y^2-2y^3-2y^2-2y+y^2+y+1\\ =y^4-y^3-y+1\end{array}$

Hence, the required multiplication is $y^4-y^3-y+1$ .