9-3:MULTIPLYINGBINOMIALSLessonObjectives:

• Multiplybinomials• Multiplytrinomialsbybinomials

OnewaytoorganizemultiplyingtwobinomialsistouseFOIL,whichstandsfor“First,Outer,Inner,Last.”ThetermFOILisamemorydeviceforapplyingtheDistributivePropertytotheproductoftwobinomials.EXAMPLE1:MULTIPLYINGUSINGFOILSimplify.1. 3x + 4( ) 2x + 5( ) 2. 3x − 4( ) 2x + 5( ) 3. 3x + 4( ) 2x − 5( ) 4. 3x − 4( ) 2x − 5( ) 5. 4x + 2( ) 3x −1( ) 6. 6x − 5( ) 3x +1( ) 7. 3x − 4( ) 3x +1( ) 8. 3x + 4( ) 3x − 4( ) 9. d + 9( ) d −11( ) 10. b+3( ) 2b− 5( ) 11. 2x − 5( ) x − 4( ) 12. 2x −3y( ) 4x +3y( )

YII a a a

i

EXAMPLE2:APPLYINGMULTIPLICATIONOFPOLYNOMIALSFindtheareaoftheshadedregions.13. 14.15.

16.Thewidthofarectangularpaintingis3in.morethantwicetheheight.Aframethatis2.5in.widegoesaroundthepainting. a)Writeanexpressionforthecombinedareaofthepaintingandframe. b)Usetheexpressiontofindthecombinedareawhentheheightofthepaintingis12in. c)Usetheexpressiontofindthecombinedareawhentheheightofthepaintingis15in.

111 111 ifAshaded_Aoutside Ainside Ashaded Aout side

3 121241 5 81162 5 1 6162.311 2 x 133 30 7,014,8 16 5 2 307612 2 t 3 202 21 16 tf 3

5x2 2 e25x2t28xt1

Ashaded.Ao AI2 m

Xt 2 Xcx21

2x 2 2 2 x 23212 2 12 t2xx2t2

b A121 242171842 402881 216140544 in

17.TheRobertsonsputarectangularpoolwithastonewalkwayarounditintheirbackyard.Thetotallengthofthepoolandwalkwayis3timesthetotalwidth.Thewalkwayis2ft.wideallaround. a)Writeanexpressionfortheareaofthepool. b)Findtheareaofthepoolwhenthetotalwidthis10ft. c)Findtheareaofthepoolwhenthetotalwidthis9ft.18.TheCuttingEdgeframeshopmakesamathbycuttingouttheinsideofarectangularboard.Usethediagramtofindthelengthandwidthoftheoriginalboardiftheareaofthematis184in2.

FOILworkswhenyoumultiplytwobinomialsbutitisnothelpfulwhenmultiplyingatrinomialandabinomial.YoucanusetheDistributivePropertytwofindtheSIXproductsandthensimplify.EXAMPLE3:MULTIPLYINGATRINOMIALANDABINOMIALSimplify.19. 2x + 7( ) 3x2 − 2x +3( ) 20. 6n−8( ) 2n2 + n+ 7( ) 21. x +1( ) x2 + x −1( )

atx

b Allo 3 101216401116156112

260 3 27

Ashaded Aoutside Ainside 158 2323118 fax2 412716 3 24 278 7282 213 24 2 4 28

IYIItf Itt t 27inx23in

12x.tY_184

m mke e

6 3 42111 21214 21 12h't't n14281566 3 1 2 872 12n3_ion2t34n

22. 2b−1( ) b2 −3b+ 4( ) 23. 2y−3( ) 2y2 + y− 4( ) 24. x2 − 7x +1( ) 2x − 9( ) 25. x −3( ) x2 + 4x + 4( ) 26. 2n−3( ) n2 − 2n+ 5( ) 27. 5x − 6( ) 4x2 − 7x + 6( )