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Chapter 5: Q.187 (page 536)

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

y+9y+3

Short Answer

Expert verified

The product of the given binomials isy2+12y+27

Step by step solution

01

Step 1. Given Information

The given binomials are y+9y+3

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

02

Part (a) Step 1. Using distributive property

According to distributive property:

y+9y+3=yy+3+9y+3y+9y+3=y2+3y+9y+27y+9y+3=y2+12y+27

03

Part (a) Step 2. Conclusion

The product of the binomials isy2+12y+27

04

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:

y+9y+3=yy+y3+9y+93y+9y+3=y2+3y+9y+27y+9y+3=y2+12y+27

05

Part (b) Step 2. Conclusion

The product of the binomials isy2+12y+27

06

Part (c) Step 1. Using Vertical Method

Multiplying the binomials using vertical method:

y+9脳y+33y+27y2+9yy2+12y+27

07

Part (c) Step 2. Conclusion

The product of the binomials isy2+12y+27

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