Chapter 5: Q.189 (page 536)

In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method
$(7 q + 4) (3 q - 8)$

Short Answer

Expert verified

The product of the given binomials is $21 q^{2} - 44 q - 32$

Step by step solution

Step 1. Given Information

The given binomials are $(7 q + 4) (3 q - 8)$

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:

$(7 q + 4) (3 q - 8) = 7 q (3 q - 8) + 4 (3 q - 8) (7 q + 4) (3 q - 8) = 7 q (3 q) - 7 q (8) + 4 (3 q) - 4 (8) (7 q + 4) (3 q - 8) = 21 q^{2} - 56 q + 12 q - 32 (7 q + 4) (3 q - 8) = 21 q^{2} - 44 q - 32$

Part (a) Step 2. Conclusion

The product of the binomials is $21 q^{2} - 44 q - 32$

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:

$(7 q + 4) (3 q - 8) = (7 q) (3 q) + (7 q) (- 8) + (4) (3 q) + (4) (- 8) (7 q + 4) (3 q - 8) = 21 q^{2} - 56 q + 12 q - 32 (7 q + 4) (3 q - 8) = 21 q^{2} - 44 q - 32$

Part (b) Step 2. Conclusion

The product of the binomials is $21 q^{2} - 44 q - 32$

Part (c) Step 1. Using Vertical Method

Multiplying the binomials using vertical method:

$\begin{matrix} 7 q & + 4 \\ \times & 3 q & - 8 \\ - 56 q & - 32 \\ 21 q^{2} & + 12 q \\ 21 q^{2} & - 44 q & - 32 \end{matrix}$

Part (c) Step 2. Conclusion

The product of the binomials is $21 q^{2} - 44 q - 32$

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In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method
$(7 q + 4) (3 q - 8)$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Using distributive property

Part (a) Step 2. Conclusion

Part (b) Step 1. Using FOIL Method

Part (b) Step 2. Conclusion

Part (c) Step 1. Using Vertical Method

Part (c) Step 2. Conclusion

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In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method7q+43q-8

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Using distributive property

Part (a) Step 2. Conclusion

Part (b) Step 1. Using FOIL Method

Part (b) Step 2. Conclusion

Part (c) Step 1. Using Vertical Method

Part (c) Step 2. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

In the following exercises, multiply the binomials using a) the Distributive Property; b) the FOIL method; c) the Vertical Method
$(7 q + 4) (3 q - 8)$