Q.212 - Intermediate Algebra

Question

In the following exercises, multiply. Use either Method.

$\left(w-7\right)\left(w^2-9w+10\right)$

Step-by-Step Solution

Answer

The product of the given polynomials is $w^3-16w^2+73w-70$

Step 1. Given Information

The given polynomials are $\left(w-7\right)\left(w^2-9w+10\right)$

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:

$$\begin{gathered} \left(w-7\right)\left(w^2-9w+10\right)=w\left(w^2-9w+10\right)-7\left(w^2-9w+10\right) \\ \left(w-7\right)\left(w^2-9w+10\right)=w^3-9w^2+10w-7w^2+63w-70 \\ \left(w-7\right)\left(w^2-9w+10\right)=w^3-16w^2+73w-70 \end{gathered}$$

Step 3. Conclusion

The product of the polynomials is $w^3-16w^2+73w-70$