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enrichment: trinomial expansions · 2018. 3. 29. · number and algebra 449 4 :mevcy i]z [daadl^c\#...

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  • Enrichment: Trinomial expansions · 2018. 3. 29. · Number and Algebra 449 4 :meVcY i]Z [daadl^c\# Fluency a x ' x * b b ( b ) c t - t , d p + p + e x . x + f d &* d ) g a & a ,
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Number and Algebra 449 Fluency 4 Yfiƒu/x4“|y4z¥¢¢¥›}/{B a <x *4F=<x *4I=4 b4 <b4*4G=<b4*4H=4 c4<t *4L=<t4*4K= d <p4*4J=<p4*4J=44 e4 <x4*4M=<x4*4J=4 f4 <d4*4EI=<d *4H= g <a *4E=<a4*4K=4 h4 <y4*4ED=<y4*4F=4 i4 <m4*4H=<m4*4EF= 5 Yfiƒu/x4“|y4z¥¢¢¥›}/{B a <x4*4G=<x,H=4 b4 <x4*4I=<x,F=4 c4<x4*4H=<x,L= d <x,J=<x4*4F=4 e4 <x,E=<x4*4ED=4 f4 <x,K=<x4*4M= g <x,F=<x4*4K=4 h4 <x,E=<x,F=4 i4 <x,H=<x,I= j <Hx4*4G=<Fx4*4I=4 k4 <Gx4*4F=<Fx4*4E=4 l4 <Gx4*4E=<Ix4*4H= m <Fx,G=<Gx4*4I=4 n4 <Lx,G=<Gx4*4H=44 o4 <Gx,F=<Fx4*4E= p <Ix4*4F=<Fx,K=4 q4 <Fx4*4G=<Gx,F=4 r4 <Hx4*4E=<Hx,I= s <Gx,F=<Jx,I=4 t4 <Ix,F=<Gx,E=4 u4 <Kx,G=<Gx,H= 6 Yfiƒu/x4“|y'y4v}/¥£}u¢4ƒ¤¥x«w“'B a <a4*4b=<a *4c=4 b4 <a,b=<a4*4c=4 c4<b,a=<a4*4c= d <x,y=<y,z=4 e4 <y,x=<z,y=4 f4 <E,x=<E4*4y= g <Fx4*4y=<x,Fy=4 h4 <Fa4*4b=<a,b=4 i4 <Gx,y=<Fx4*4y= j <Fa,b=<Ga4*4F=4 k4 <Hx,Gy=<Gx,Hy=4 l4 <xy,yz=<z *4Gx= Example 1a Example 1b,c,d Problem-solving 7 U4¤¥¥£4}/4u4|¥«'y4›}“|4x}£y/'}¥/'4H4£4vfl4I4£4}'4“¥4vy4yfi“y/xyxB4V¥“|4“|y4¢y/{“|4u/x4›}x“|4u¤y4 “¥4vy4}/w¤yu'yx4vfl4x4£B a Z}/x4u/4yfiƒu/xyx4yfiƒ¤y''}¥/4z¥¤4“|y4u¤yu4¥z4“|y4/y›4¤¥¥£B b ]z4x4<4GN i Ù/x4“|y4u¤yu4¥z4“|y4/y›4¤¥¥£ ii vfl4|¥›4£«w|4|u'4“|y4u¤yu4}/w¤yu'yxS ISBN 978-0-521-17865-5 Photocopying is restricted under law and this material must not be transferred to another party. © Greenwood et al. 2011 Cambridge University Press Chapter 8 Algebraic techniques 450 Enrichment: Trinomial expansions 12 i'}/{4“|y4x}'“¤}v«“}‹y4¢u›4<a4*4b=<c4*4d *4e=4<4ac4*4ad4*4ae4*4bc4*4bd4*4beB i'y4“|}'4¡/¥›¢yx{y4“¥4yfiƒu/x4u/x4'}£ƒ¢}zfl4“|y'y4ƒ¤¥x«w“'B4b¥“yN4x4·4x F 4<4x G B a <x4*4E=<x F 4*4x4*4E=4 b4 <x4,4F=<x F 4,4x4*4G= c <Fx4,4E=<Fx F 4,4x4*4H=4 d4 <x F 4,4x4*4E=<x4*4G= e <Ix F 4,4x4*4F=<Fx4,4G=4 f4 <Fx F 4,4x *4K=<Hx4,4K= g <x4*4a=<x F 4,4ax4*4a=4 h4 <x4,4a)<x F 4,4ax4,4a F = i <x4*4a=<x F 4,4ax *4a F =4 j4 <x4,4a)<x F 4*4ax4*4a F = 13 b¥›4“¤fl4“¥4yfiƒu/x4<x4*4E=<x4*4F=<x4*4G=B 10 k¤}“y4“|y4£}''}/{4“y¤£'4}/4“|y'y4yfiƒu/'}¥/'B a <x4*4F=<x4*4ss4=4<4x F 4*4Ix4*4J4 b4 <x4*4ss4=<x *4I=4<4x F 4*4Kx4*4ED c <x4*4E=<x4*4ss4=4<4x F 4*4Kx4*4ss4 d4 <x4*4ss4=<x4*4M=4<4x F 4*4EEx4*4ss e <x *4G=<x4,4ss4=4<4x F 4*4x4,4ss4 f4 <x ,4I=<x4*4ss4=4<4x F 4,4Fx4,4ss g <x4*4E=<4ss4*4G=4<4Fx F 4*4ss4*4ss4 h4 <4ss4,4H=<Gx4,4E=4<4Mx F 4,4ss4*4ss i <x4*4F=<4ss4*4ss4=4<4Kx F 4*4ss4*4J4 j4 <4ss4,4ss4=<Fx4,4E=4<4Jx F 4,4ss4*4H 11 W¥/'}xy¤4“|y4v}/¥£}u¢4ƒ¤¥x«w“4<x4*4a=<x4*4b=B4Z}/x4“|y4ƒ¥''}v¢y4}/“y{y¤4‹u¢«y'4¥z4a4u/x4b4}zN a <x4*4a=<x4*4b=4<4x F 4*4Ix4*4J b <x4*4a=<x4*4b=4<4x F 4,4Ix4*4J c <x4*4a=<x4*4b=4<4x F 4*4x4,4J d <x4*4a=<x4*4b=4<4x F 4,4x,J Reasoning Problem-solving 8 U4ƒ}w“«¤y4z¤u£y4I4w£4›}xy4|u'4u4¢y/{“|4›|}w|4}'4“›}wy4“|y44 ›}x“|4x4w£B a Z}/x4u/4yfiƒ¤y''}¥/4z¥¤4“|y4“¥“u¢4u¤yu4¥z4“|y4z¤u£y4u/x4 ƒ}w“«¤yB b Z}/x4u/4yfiƒ¤y''}¥/4}/4yfiƒu/xyx4z¥¤£4z¥¤4“|y4u¤yu4¥z4“|y4 ƒ}w“«¤y4¥/¢flB 9 h|y4¥«“'}xy4yx{y4¥z4u4ƒu“|4u¤¥«/x4u4¤yw“u/{«¢u¤4'›}££}/{44 ƒ¥¥¢4}'4EI4£4¢¥/{4u/x4ED4£4›}xyB4h|y4ƒu“|4}'4x4£y“¤y'4›}xyB a Z}/x4u/4yfiƒ¤y''}¥/4z¥¤4“|y4u¤yu4¥z4“|y4ƒ¥¥¢4}/4yfiƒu/xyx4z¥¤£B b Z}/x4“|y4u¤yu4¥z4“|y4ƒ¥¥¢4}z4x4<4FB 2x cm 5 cm x cm Picture 15 m 10 m x m Pool ISBN 978-0-521-17865-5 Photocopying is restricted under law and this material must not be transferred to another party. © Greenwood et al. 2011 Cambridge University Press

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Page 1: Enrichment: Trinomial expansions · 2018. 3. 29. · Number and Algebra 449 4 :meVcY i]Z [daadl^c\# Fluency a x ' x * b b ( b ) c t - t , d p + p + e x . x + f d &* d ) g a & a ,

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ISBN 978-0-521-17865-5 Photocopying is restricted under law and this material must not be transferred to another party.

© Greenwood et al. 2011 Cambridge University Press

Chapter 8 Algebraic techniques450

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ISBN 978-0-521-17865-5 Photocopying is restricted under law and this material must not be transferred to another party.

© Greenwood et al. 2011 Cambridge University Press

Original program: a x b x c -> e1 b x c x d -> e2 c x d -> e3

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