9-4:MULTIPLYINGSPECIALCASESLessonObjectives:

• Findingthesquareofabinomial• Findingthedifferenceoftwosquares

Theexpressions a+ b( )2 and a− b( )2 aresquaresofbinomials.Tosquareabinomial,youcanuseFOILorthefollowingshortcut.RULE:THESQUAREOFABINOMIAL and Thesquareofabinomialisthesquareofthefirstterm,plustwicetheproductofthetwoterms,plusthesquareofthelastterm.EXAMPLE1:SQUARRINGABINOMIALSimplify.1. x + 4( )2 2. y−3( )2 3. y+11( )2 4. 3w− 5( )2 5. t + 6( )2 6. x − 7( )2 7. 9c−8( )2 8. 3m+ 2n( )2 9. x2 + y2( )

2 10. 2x2 + y2( )2 11. y2 − 4w2( )

2 12. 5x4 −3x2( )2

EXAMPLE2:MENTALMATHSimplifyinyourmind.13.812 14. 592 15.312

atbEtba aI btb2a2 2abtb2

Catgbkatb ja bCab

atb2 a2t2abtb a bZaZ2abtb2

µabyb2csTFn2abX2t8Xtl6y2f6y0aq.q y722y 9w23owt

t X2l4Xt gyc2_144 9m2tHmnt4thec2 6 61 36

Cx't

x4t2X2y2t 4x4t4x2y2t y 8y2w2tl6 2sxE30Xbt

80115 60 IP 30156400 160 1 3600 12011 900 60116561 3481 961

16. 292 17. 982 18. 2032

Theproductofthesumanddifferenceofthesametwotermsalsoproducesapattern. RULE:THEDIFFERENCEOFTWOSQUARESa+ b( ) a− b( ) = Theproductofthesumanddifferenceofthesametwotermsisthedifferenceoftheirsquares.EXAMPLE3:FINDINGTHEDIFFERENCEOFTWOSQUARESSimplify.19. x + 4( ) x − 4( ) 20. 3x − 5( ) 3x + 5( ) 21. p4 −8( ) p4 +8( ) 22. d +11( ) d −11( ) 23. c2 +8( ) c2 −8( ) 24. 9v3 +w4( ) 9v3 −w4( ) 25. x2 − 2y( ) x2 + 2y( ) 26. 3x + 4( ) 3x + 4( ) EXAMPLE4:MENTALMATHSimplifyinyourbrains.27. 18( ) 22( ) 28. 19( ) 21( ) 29. 59( ) 61( ) 30. 87( ) 93( ) 31. 96( ) 104( ) 32. 33( ) 47( )

a7qbtb230D2 10025 2003

900 60 1 toooo 40014 4000011200 9841 9604 41209

atI D a2ab ab b92 b

a2b2

p42

X qx2 2 ps d2

c4 8N6_ X4_4y

a2o 2 202 20 4601Got400 4 00 I 3600 i3960 3990 35990

90 3 9013 Goo4 10014 40740181009 toooo 16 1600 4980910 99840 15510

33.Findtheareaoftheshadedregionthatis(eventually)drawnontheboard.34.Simplify.a) x + 4( ) x +3( ) b) x + 4( ) x − 4( ) c) x − 4( )2 d) 2x − 7( ) 2x + 7( ) e) 2x −1( ) 2x +3( ) f) 2x + 5( )2

Asha

4 2112 9 x 9

412112 1 t2tf

3X2tl2Xt18units

21311 12 X2 162 7120

XI8Xt16 4 2 49

72

I4 2161 21 3 4 72 25

4 2 4 3