Q.207 - Intermediate Algebra

Question

In the following exercises, multiply using a) the Distributive Property; b) the Vertical Method

$\left(u+4\right)\left(u^2+3u+2\right)$

Step-by-Step Solution

Answer

The product of the given polynomials is $u^3+7u^2+14u+8$

Step 1. Given Information

The given polynomials are $\left(u+4\right)\left(u^2+3u+2\right)$

The product is to be determined using a) the Distributive Property; b) the Vertical Method

Part (a) Step 1. Using distributive property

According to distributive property:

$$\begin{gathered} \left(u+4\right)\left(u^2+3u+2\right)=u\left(u^2+3u+2\right)+4\left(u^2+3u+2\right) \\ \left(u+4\right)\left(u^2+3u+2\right)=u^3+3u^2+2u+4u^2+12u+8 \\ \left(u+4\right)\left(u^2+3u+2\right)=u^3+7u^2+14u+8 \end{gathered}$$

Part (a) Step 2. Conclusion

The product of the polynomials is $u^3+7u^2+14u+8$

Part (b) Step 1. Using Vertical Method

Multiplying using vertical method:

$\begin{array}{rrr}{u}^2+& 3u+& 2\\ \times & u+& 4\\ 4u^2+& 12u+& 8\\ u^3+3u^2+& 2u & \\ u^3+7u^2+& 14u+& 8\end{array}$

Part (b) Step 2. Conclusion

The product of the polynomials is $u^3+7u^2+14u+8$