Q.213 - Intermediate Algebra

Question

In the following exercises, multiply. Use either Method.

$\left(p-4\right)\left(p^2-6p+9\right)$

Step-by-Step Solution

Answer

The product of the given polynomials is $p^3-10p^2+33p-36$

Step 1. Given Information

The given polynomials are $\left(p-4\right)\left(p^2-6p+9\right)$

The product is to be determined using any method i.e. either the Distributive Property or the Vertical Method.

Step 2. Using distributive property

According to distributive property:

$$\begin{gathered} \left(p-4\right)\left(p^2-6p+9\right)=p\left(p^2-6p+9\right)-4\left(p^2-6p+9\right) \\ \left(p-4\right)\left(p^2-6p+9\right)=p^3-6p^2+9p-4p^2+24p-36 \\ \left(p-4\right)\left(p^2-6p+9\right)=p^3-10p^2+33p-36 \end{gathered}$$

Step 3. Conclusion

The product of the polynomials is $p^3-10p^2+33p-36$