ࡱ > '` R L bjbj 2 r r 2 ~ ~ ~ ~ ~ ~ ~ :' :' :' 8 r' \ ( T 'F .) * X- X- X- X- . . . D D D D D D D $ G h I L D ~ . . . . . D ~ ~ X- X- 4 E C C C . ~ X- ~ X- D C . D C C ~ ~ C X- ") O :' \A C D E 0 'F C I bB I C I ~ C . . C . . . . . D D VC L . . . 'F . . . . $ ~ ~ ~ ~ ~ ~ N0V_R 1 Џ(ulQ_l ( 1 ) a 2 - b 2 = ( a + b ) ( a - b ) ( 2 ) a 2 2 a b + b 2 = ( a b ) 2 ( 3 ) a 3 + b 3 = ( a + b ) ( a 2 - a b + b 2 ) ( 4 ) a 3 - b 3 = ( a - b ) ( a 2 + a b + b 2 ) NbQeEQQ*N8^(uvlQ_ ( 5 ) a 2 + b 2 + c 2 + 2 a b + 2 b c + 2 c a = ( a + b + c ) 2 ( 6 ) a 3 + b 3 + c 3 - 3 a b c = ( a + b + c ) ( a 2 + b 2 + c 2 - a b - b c - c a ) ( 7 ) a n - b n = ( a - b ) ( a n - 1 + a n - 2 b + a n - 3 b 2 + & + a b n - 2 + b n - 1 ) vQ-Nn :Ncktepe ( 8 ) a n - b n = ( a + b ) ( a n - 1 - a n - 2 b + a n - 3 b 2 - & + a b n - 2 - b n - 1 ) vQ-Nn :NvPpe ( 9 ) a n + b n = ( a + b ) ( a n - 1 - a n - 2 b + a n - 3 b 2 - & - a b n - 2 + b n - 1 ) vQ-Nn :NGYpe Џ(ulQ_lRV_e9hncYy_vyrp9hncW[k0|pe0cpe0&{SI{cknxp`S_0W blQ_ O1 RV_ ( 1 ) - 2 x 5 n - 1 y n + 4 x 3 n - 1 y n + 2 - 2 x n - 1 y n + 4 ( 2 ) x 3 - 8 y 3 - z 3 - 6 x y z ( 3 ) a 2 + b 2 + c 2 - 2 b c + 2 c a - 2 a b ( 4 ) a 7 - a 5 b 2 + a 2 b 5 - b 7 ( 1 ) S_= - 2 x n - 1 y n ( x 4 n - 2 x 2 n y 2 + y 4 ) = - 2 x n - 1 y n [ ( x 2 n ) 2 - 2 x 2 n y 2 + ( y 2 ) 2 ] = - 2 x n - 1 y n ( x 2 n - y 2 ) 2 = - 2 x n - 1 y n ( x n - y ) 2 ( x n + y ) 2 ( 2 ) S_= x 3 + ( - 2 y ) 3 + ( - z ) 3 - 3 x ( - 2 y ) ( - Z ) = ( x - 2 y - z ) ( x 2 + 4 y 2 + z 2 + 2 x y + x z - 2 y z ) ( 3 ) S_= ( a 2 - 2 a b + b 2 ) + ( - 2 b c + 2 c a ) + c 2 ( a - b ) 2 + 2 c ( a - b ) + c 2 = ( a - b + c ) 2 ,g\SN zRSb_vcO(ulQ_( 5 ) lYN S_= a 2 + ( - b ) 2 + c 2 + 2 ( - b ) c + 2 c a + 2 a ( - b ) = ( a - b + c ) 2 ( 4 ) S_= ( a 7 - a 5 b 2 ) + ( a 2 b 5 - b 7 ) = a 5 ( a 2 - b 2 ) + b 5 ( a 2 - b 2 ) 0 0= ( a 2 - b 2 ) ( a 5 + b 5 ) = ( a + b ) ( a - b ) ( a + b ) ( a 4 - a 3 b + a 2 b 2 - a b 3 + b 4 ) = ( a + b ) 2 ( a - b ) ( a 4 - a 3 b + a 2 b 2 - a b 3 + b 4 ) O2 RV_a 3 + b 3 + c 3 - 3 a b c bN]~wSlQ( a + b ) 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3 = ( a + b ) 3 - 3 a b ( a + b ) S_= ( a + b ) 3 - 3 a b ( a + b ) + c 3 - 3 a b c = ;( a + b ) 3 + c 3 =- 3 a b ( a + b + c ) = ( a + b + c ) ;( a + b ) 2 - c ( a + b ) + c 2 ] - 3 a b ( a + b + c ) = ( a + b + c ) ( a 2 + b 2 + c 2 - a b - b c - c a ) O3 RV_x 1 5 + x 1 4 + x 1 3 + & + x 2 + x + 1 Rg ُ*NYy_vyrp/f g1 6 yN gؚ!kyx 1 5 _Yx v!kpez!kQ0 1udk`0R^(ulQ_a n - b n egR x 1 6 - 1 = ( x - 1 ) ( x 1 5 + x 1 4 + x 1 3 + & x 2 + x + 1 ) 0 I N C L U D E P I C T U R E " h t t p : / / r e s 3 . p u d o n g - e d u . s h . c n / R E S O U R C E / C Z / C Z S X / S X B L / S X T S 1 0 1 9 / _ O L E 7 7 4 7 . J P G " \ * M E R G E F O R M A T I N E T 0 0f (W,gvRǏz-N(u0RHQXNN( x - 1 ) QdN( x - 1 ) vb]ُ Nb](WI{_Sb_-N_8^(u 02 by0myl 0 0V_R/fYy_XNlvЏ{(WYy_XNlЏ{etet0S{8^\Q*NT{|yTv^:N Nyb\$N*NN&{SvSvT{|yvNbm:N(W[gNYy_RV_e b` YNTv^bvNbmvysSbYy_-Nvg Nybb$NybYyb(WYy_-Nm N$N*NN&{TvSvyMRy:NbyTy:Nmyby0myvvv/fOYy_(uR~RlۏLV_R 0 0O4 RV_x 3 - 9 x + 8 l1 \8^pey8 bb- 1 + 9 S_= x 3 - 9 x - 1 + 9 = ( x 3 - 1 ) - 9 x + 9 = ( x - 1 ) ( x 2 + x + 1 ) - 9 ( x - 1 ) = ( x - 1 ) ( x 2 + x - 8 ) l2 \ N!ky- 9 x bb- x - 8 x S_= x 3 - x - 8 x + 8 = ( x 3 - x ) + ( - 8 x + 8 ) = x ( x + 1 ) ( x - 1 ) - 8 ( x - 1 ) = ( x - 1 ) ( x 2 + x - 8 ) l3 \ N!kyx 3 bb9 x 3 - 8 x 3 S_= 9 x 3 - 8 x 3 - 9 x + 8 = ( 9 x 3 - 9 x ) + ( - 8 x 3 + 8 ) = 9 x ( x + 1 ) ( x - 1 ) - 8 ( x - 1 ) ( x 2 + x + 1 ) = ( x - 1 ) ( x 2 + x - 8 ) l4 mR$Ny- x 2 + x 2 S_= x 3 - 9 x + 8 = x 3 - x 2 + x 2 - 9 x + 8 = x 2 ( x - 1 ) + ( x - 8 ) ( x - 1 ) O5 RV_ ( 1 ) x 9 + x 6 + x 3 - 3 ( 2 ) ( m 2 - 1 ) ( n 2 - 1 ) + 4 m n ( 3 ) ( x + 1 ) 4 + ( x 2 - 1 ) 2 + ( x - 1 ) 4 ( 4 ) a 3 b - a b 3 + a 2 + b 2 + 1 ( 1 ) \- 3 bb- 1 - 1 - 1 S_= x 9 + x 6 + x 3 - 1 - 1 - 1 = ( x 9 - 1 ) + ( x 6 - 1 ) + ( x 3 - 1 ) = ( x 3 - 1 ) ( x 6 + x 3 + 1 ) + ( x 3 - 1 ) ( x 3 + 1 ) + ( x 3 - 1 ) = ( x 3 - 1 ) ( x 6 + 2 x 3 + 3 ) = ( x - 1 ) ( x 2 + x + 1 ) ( x 6 + 2 x 3 + 3 ) ( 2 ) \4 m n bb2 m n + 2 m n S_= ( m 2 - 1 ) ( n 2 - 1 ) + 2 m n + 2 m n = m 2 n 2 - m 2 - n 2 + 1 + 2 m n + 2 m n = ( m 2 n 2 + 2 m n + 1 ) - ( m 2 - 2 m n + n 2 ) = ( m n + 1 ) 2 - ( m - n ) 2 = ( m n + m - n + 1 ) ( m n - m + n + 1 ) 0 0( 3 ) \( x 2 - 1 ) 2 bb2 ( x 2 - 1 ) 2 - ( x 2 - 1 ) 2 0 0S_= ( x + 1 ) 4 + 2 ( x 2 - 1 ) 2 - ( x 2 - 1 ) 2 + ( x - 1 ) 4 0= ;( x + 1 ) 4 + 2 ( x + 1 ) 2 ( x - 1 ) 2 + ( x - 1 ) 4 ] - ( x 2 - 1 ) 2 = ;( x + 1 ) 2 + ( x - 1 ) 2 ] 2 - ( x 2 - 1 ) 2 = ( 2 x 2 + 2 ) 2 - ( x 2 - 1 ) 2 = ( 3 x 2 + 1 ) ( x 2 + 3 ) ( 4 ) mR$Ny+ a b - a b 0 0S_= a 3 b - a b 3 + a 2 + b 2 + 1 + a b - a b = ( a 3 b - a b 3 ) + ( a 2 - a b ) + ( a b + b 2 + 1 ) = a b ( a + b ) ( a - b ) + a ( a - b ) + ( a b + b 2 + 1 ) = a ( a - b ) ;b ( a + b ) + 1 ] + ( a b + b 2 + 1 ) = [ a ( a - b ) + 1 ] ( a b + b 2 + 1 ) = ( a 2 - a b + 1 ) ( b 2 + a b + 1 ) 03 bcCQl 0bcCQlcv/f\ N*N YBgvNpe_-Nvg NRw\O N*NteSOv^(u N*NevW[kfNُ*NteSOegЏ{NOЏ{Ǐz{fnpf O6 RV_( x 2 + x + 1 ) ( x 2 + x + 2 ) - 1 2 Rg \S_U\ _/fsQNx vV!kYy_RV_VbN NY\x 2 + x w\O N*NteSOv^(uW[ky egfNN/fSlS:NsQNy vN!k Ny_vV_RN x 2 + x = y R 0S_= ( y + 1 ) ( y + 2 ) - 1 2 = y 2 + 3 y - 1 0 = ( y - 2 ) ( y + 5 ) = ( x 2 + x - 2 ) ( x 2 + x + 5 ) = ( x - 1 ) ( x + 2 ) ( x 2 + x + 5 ) 0f ,g_NS\x 2 + x + 1 w\O N*NteSOkYNx 2 + x + 1 = u O7 RV_( x 2 + 3 x + 2 ) ( 4 x 2 + 8 x + 3 ) - 9 0 S_= ( x + 1 ) ( x + 2 ) ( 2 x + 1 ) ( 2 x + 3 ) - 9 0 = [ ( x + 1 ) ( 2 x + 3 ) ] [ ( x + 2 ) ( 2 x + 1 ) ] - 9 0 = ( 2 x 2 + 5 x + 3 ) ( 2 x 2 + 5 x + 2 ) - 9 0 Ny = 2 x 2 + 5 x + 2 RS_= y ( y + 1 ) - 9 0 = y 2 + y - 9 0 = ( y + 1 0 ) ( y - 9 ) = ( 2 x 2 + 5 x + 1 2 ) ( 2 x 2 + 5 x - 7 ) = ( 2 x 2 + 5 x + 1 2 ) ( 2 x + 7 ) ( x - 1 ) f [Yy_S_vR`I{Sb_/fbN~b0ReCQ( y ) vW@x O8 RV_( x 2 + 4 x + 8 ) 2 + 3 x ( x 2 + 4 x + 8 ) + 2 x 2 x 2 + 4 x + 8 = y RS_= y 2 + 3 x y + 2 x 2 = ( y + 2 x ) ( y + x ) = ( x 2 + 6 x + 8 ) ( x 2 + 5 x + 8 ) = ( x + 2 ) ( x + 4 ) ( x 2 + 5 x + 8 ) f 1u,gSw(ubcCQlRV_e N_\S_-NvCQ(ueCQNbc9hncv _eQ_veCQS_-NvSCQTeSCQSN NwSb_bcCQlv,g(/f{SYy_ O9 RV_6 x 4 + 7 x 3 - 3 6 x 2 - 7 x + 6 l S_= 6 ( x 4 + 1 ) 7 x ( x 2 - 1 ) - 3 6 x 2 = 6 ;( x 4 - 2 x 2 + 1 ) + 2 x 2 =+ 7 x ( x 2 - 1 ) - 3 6 x 2 = 6 [ ( x 2 - 1 ) 2 + 2 x 2 ] + 7 x ( x 2 - 1 ) - 3 6 x 2 = 6 ( x 2 - 1 ) 2 + 7 x ( x 2 - 1 ) - 2 4 x 2 = [ 2 ( x 2 - 1 ) - 3 x =;3 ( x 2 - 1 ) + 8 x ] = ( 2 x 2 - 3 x - 2 ) ( 3 x 2 + 8 x - 3 ) = ( 2 x + 1 ) ( x - 2 ) ( 3 x - 1 ) ( x + 3 ) 0 0f ,gl[E N/f\x 2 - 1 w\O N*NteSOFOv^l gzeCQegNf[sSq~O(ubcCQlTv^^kneCQegNfteSO O1 0 RV_( x 2 + x y + y 2 ) - 4 x y ( x 2 + y 2 ) 0 0Rg ,g+T g$N*NW[kNS_Nbcُ$N*NW[kvMOneYy_Oc NSُ7hvYy_S\ONCQ[y_[NR㉄vNCQ[y_~8^Nu = x + y v = x y (ubcCQlRV_ S_= [ ( x + y ) 2 - x y ] 2 - 4 x y [ ( x + y ) 2 - 2 x y ] Nx + y = u x y = v R S_= ( u 2 - v ) 2 - 4 v ( u 2 - 2 v ) = u 4 - 6 u 2 v + 9 v 2 = ( u 2 - 3 v ) 2 = ( x 2 + 2 x y + y 2 - 3 x y ) 2 = ( x 2 - x y + y 2 ) 2 N0Npe_vBl