Q.208 - Intermediate Algebra

Question

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

$\left(y+8\right)\left(4y^2+y-7\right)$

Step-by-Step Solution

Answer

The product of the given polynomials is $4y^3+33y^2+y-56$

Step 1. Given Information

The given polynomials are $\left(y+8\right)\left(4y^2+y-7\right)$

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:

$$\begin{gathered} \left(y+8\right)\left(4y^2+y-7\right)=y\left(4y^2+y-7\right)+8\left(4y^2+y-7\right) \\ \left(y+8\right)\left(4y^2+y-7\right)=4y^3+y^2-7y+32y^2+8y-56 \\ \left(y+8\right)\left(4y^2+y-7\right)=4y^3+33y^2+y-56 \end{gathered}$$

Part (a) Step 2. Conclusion

The product of the polynomials is $4y^3+33y^2+y-56$

Part (b) Step 1. Using Vertical Method

Multiplying using vertical method:

$\begin{array}{rrr}4y^2+& y-& 7\\ \times & y+& 8\\ 32y^2+& 8y-& 56\\ 4y^3+y^2-& 7y & \\ 4y^3+33y^2+& y-& 56\end{array}$

Part (b) Step 2. Conclusion

The product of the polynomials is $4y^3+33y^2+y-56$