Q.209 - Intermediate Algebra

Question

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

$\left(a+10\right)\left(3a^2+a-5\right)$

Step-by-Step Solution

Answer

The product of the given polynomials is $3a^3+31a^2+5a-50$

Step 1. Given Information

The given polynomials are $\left(a+10\right)\left(3a^2+a-5\right)$

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:

$$\begin{gathered} \left(a+10\right)\left(3a^2+a-5\right)=a\left(3a^2+a-5\right)+10\left(3a^2+a-5\right) \\ \left(a+10\right)\left(3a^2+a-5\right)=3a^3+a^2-5a+30a^2+10a-50 \\ \left(a+10\right)\left(3a^2+a-5\right)=3a^3+31a^2+5a-50 \end{gathered}$$

Part (a) Step 2. Conclusion

The product of the polynomials is $3a^3+31a^2+5a-50$

Part (b) Step 1. Using Vertical Method

Multiplying using vertical method:

$\begin{array}{rrr}3a^2+& a-& 5\\ \times & a+& 10\\ 30a^2+& 10a-& 50\\ 3a^3+ a^2-& 5a & \\ 3a^3+31a^2+& 5a-& 50\end{array}$

Part (b) Step 2. Conclusion

The product of the polynomials is $3a^3+31a^2+5a-50$