Question

In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method

$\left(4p+11\right)\left(5p-4\right)$

Short answer

The product of the given binomials is$20p^2+39p-44$

Step-by-step solution

Step 1. Given Information

The given binomials are $\left(4p+11\right)\left(5p-4\right)$

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

Part (a) Step 1. Using distributive property

According to distributive property:

$$\begin{gathered} \left(4p+11\right)\left(5p-4\right)=4p\left(5p-4\right)+11\left(5p-4\right) \\ \left(4p+11\right)\left(5p-4\right)=4p\left(5p\right)\mathit{-}4p\left(\mathrm{4}\right)+11\left(5p\right)-11\left(4\right) \\ \left(4p+11\right)\left(5p-4\right)=20p^2-16p+55p-44 \\ \left(4p+11\right)\left(5p-4\right)=20p^2+39p-44 \end{gathered}$$

Part (a) Step 2. Conclusion

The product of the binomials is$20p^2+39p-44$

Part (b) Step 1. Using FOIL Method

Using FOIL method, the terms are multiplied in the order of First Terms, Outer Terms, Inner Terms and then Last Terms:

$$\begin{gathered} \left(4p+11\right)\left(5p-4\right)=\left(4p\right)\left(5p\right)+\left(4p\right)\left(-4\right)+\left(11\right)\left(5p\right)+\left(11\right)\left(-4\right) \\ \left(4p+11\right)\left(5p-4\right)=20p^2-16p+55p-44 \\ \left(4p+11\right)\left(5p-4\right)=20p^2+39p-44 \end{gathered}$$

Part (b) Step 2. Conclusion

The product of the binomials is$20p^2+39p-44$

Part (c) Step 1. Using Vertical Method

Multiplying the binomials using vertical method:

$\begin{array}{ccc}& 4p& +11\\ \times & 5p& -4\\ & -16p& -44\\ 20p^2& +55p& \\ 20p^2& +39p& -44\end{array}$

Part (c) Step 2. Conclusion

The product of the binomials is$20p^2+39p-44$