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展開 No.1展開 No.1 次の式を展開しなさい。次の式を展開しなさい。

11 xx++ 2y2y(( )) (( ))33 22 aa++ 11 aa -- 22 ((aa -- aa++ 11 ((aa ++ 2a2a++ 44))(( )) (( ))(( )) 22 )) 22

33 2a2a -- 3b3b ((4a4a ++ 6ab6ab++ 9b9b(( )) (( )) 22 22)) 44 ((qq -- qq++ 22 ((qq ++ qq -- 22(( )) 22 )) 22 ))

55 aa++ bb -- cc(( )) (( ))22 66 aa++ 2b2b aa -- 2b2b(( )) (( ))22(( ))22

77 ((pp ++ pp -- 11 ((pp -- pp -- 11(( )) 22 )) 22 )) 88 xx++ 22 ((xx -- 2x2x++ 44(( )) (( )) 22 ))

99 xx -- 11 ((xx -- 22 xx -- 33 ((xx -- 44(( )) (( )) ))(( )) )) 1010 aa++ 33(( )) (( ))33

1111 ((xx -- 3x3x++ 11 ((xx ++ 3x3x -- 11(( )) 22 )) 22 )) 1212 xx++ yy ((xx ++ yy xx -- yy(( )) (( )) 22 22))(( ))

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展開 No.1（解答）展開 No.1（解答）

11 xx++ 2y2y(( )) (( ))33

== xx ++ 33 ⋅⋅ xx ⋅⋅ 2y2y++ 33 ⋅⋅ xx ⋅⋅ 2y2y ++ 2y2y33 22 (( ))22 (( ))33

== xx ++ 6x6x yy++ 12xy12xy ++ 8y8y33 22 22 33

22 aa++ 11 aa -- 22 ((aa -- aa++ 11 ((aa ++ 2a2a++ 44))(( )) (( ))(( )) 22 )) 22

== ((aa ++ 11 ((aa -- 8833 )) 33 ))

== aa -- 7a7a -- 8866 33

33 2a2a -- 3b3b ((4a4a ++ 6ab6ab++ 9b9b == 8a8a -- 27b27b(( )) (( )) 22 22)) 33 33 44 ((qq -- qq++ 22 ((qq ++ qq -- 22(( )) 22 )) 22 ))

== qq -- qq -- 22 }}((qq ++ qq -- 22)){{ 22 (( )) 22

== qq -- qq -- 2244 (( ))22

== qq -- ((qq -- 4q4q++ 4444 22 ))

== qq -- qq ++ 4q4q -- 4444 22

55 aa++ bb -- cc(( )) (( ))22

== aa++ bb -- 22 aa++ bb cc++ cc(( ))22 (( )) 22

== aa ++ 2ab2ab++ bb -- 2ac2ac -- 2bc2bc++ cc22 22 22

== aa ++ bb ++ cc ++ 2ab2ab -- 2bc2bc -- 2ca2ca22 22 22

66 aa++ 2b2b aa -- 2b2b(( )) (( ))22(( ))22

== aa++ 2b2b aa -- 2b2b }}{{(( ))(( )) 22

== aa -- 4b4b }}{{ 22 22 22

== aa -- 8a8a bb ++ 16b16b44 22 22 44

77 ((pp ++ pp -- 11 ((pp -- pp -- 11(( )) 22 )) 22 ))

== ((pp -- 11 ++ pp ((pp -- 11-- pp22 )) 22 ))

== ((pp -- 11 -- pp22 ))22 22

== pp -- 2p2p ++ 11-- pp44 22 22

== pp -- 3p3p ++ 1 1 44 22

88 xx++ 22 ((xx -- 2x2x++ 44 == xx ++ 88(( )) (( )) 22 )) 33

99 xx -- 11 ((xx -- 22 xx -- 33 ((xx -- 44(( )) (( )) ))(( )) ))== xx -- 11 xx -- 44 xx -- 22 xx -- 33(( ))(( ))(( ))(( ))

== ((xx -- 5x5x++ 44 ((xx -- 5x5x++ 6622 )) 22 ))

== ((xx -- 5x5x ++ 66((xx -- 5x5x ++ 44((xx -- 5x5x ++ 242422 ))22 22 )) 22 ))

== xx -- 10x10x ++ 25x25x ++ 10x10x -- 50x50x++ 242444 33 22 22

== xx -- 10x10x ++ 35x35x -- 50x50x++ 242444 33 22

1010 aa++ 33 == aa ++ 9a9a ++ 27a27a++ 2727(( )) (( ))33 33 22

1111 ((xx -- 3x3x++ 11 ((xx ++ 3x3x -- 11(( )) 22 )) 22 ))

== xx -- 3x3x -- 11 }}((xx ++ 3x3x -- 11)){{ 22 (( )) 22

== xx -- 3x3x -- 1144 (( ))22

== xx -- ((9x9x -- 6x6x++ 1144 22 ))

== xx -- 9x9x ++ 6x6x -- 1144 22

1212 xx++ yy ((xx ++ yy xx -- yy(( )) (( )) 22 22))(( ))

== xx++ yy xx -- yy ((xx ++ yy(( ))(( )) 22 22))

== ((xx -- yy ((xx ++ yy22 22)) 22 22))

== xx -- yy44 44




11 pp -- 22 ((pp++ 22 pp++ 11 ((pp++ 55(( )) (( )) ))(( )) )) 22 xx++ yy++ zz xx++ yy -- zz(( )) (( ))(( ))

33 2x2x++ yy ((4x4x -- 2xy2xy++ yy(( )) (( )) 22 22)) 44 xx -- 22 xx++ 33 ((xx ++ 2x2x++ 44 ((xx -- 3x3x++ 99))(( )) (( ))(( )) 22 )) 22

55 pp++ 22(( )) (( ))33 66 aa -- 33 ((aa ++ 3a3a++ 99(( )) (( )) 22 ))

77 aa -- bb -- cc ((aa++ bb -- cc(( )) (( )) )) 88 ((aa ++ 2a2a -- 33 ((aa -- 2a2a++ 33(( )) 22 )) 22 ))

99 xx -- 2y2y(( )) (( ))33 1010 xx++ yy++ zz(( )) (( ))22

1111 ((xx -- 11 ((xx ++ 22 ((xx ++ 11))((xx -- 22))(( )) 22 )) 22 )) 22 22 1212 3q3q++ 2r2r 3q3q -- 2r2r(( )) (( ))22(( ))22




11 pp -- 22 ((pp++ 22 pp++ 11 ((pp++ 55(( )) (( )) ))(( )) ))== pp -- 22 ((pp++ 55 ((pp++ 22 pp++ 11(( )) )) ))(( ))

== ((pp ++ 3p3p -- 1010 ((pp ++ 3p3p++ 2222 )) 22 ))

== ((pp ++ 3p3p ++ 22((pp ++ 3p3p -- 1010((pp ++ 3p3p -- 202022 ))22 22 )) 22 ))

== pp ++ 6p6p ++ 9p9p -- 8p8p -- 24p24p -- 202044 33 22 22

== pp ++ 6p6p ++ pp -- 24p24p -- 202044 33 22

22 xx++ yy++ zz xx++ yy -- zz(( )) (( ))(( ))

== xx++ yy -- zz(( ))22 22

== xx ++ 2xy2xy++ yy -- zz22 22 22

33 2x2x++ yy ((4x4x -- 2xy2xy++ yy == 8x8x ++ yy(( )) (( )) 22 22)) 33 33 44 xx -- 22 xx++ 33 ((xx ++ 2x2x++ 44 ((xx -- 3x3x++ 99))(( )) (( ))(( )) 22 )) 22

== xx -- 22 ((xx ++ 2x2x++ 44 xx++ 33 ((xx -- 3x3x++ 99))(( )) 22 ))(( )) 22

== ((xx -- 88 ((xx ++ 272733 )) 33 ))

== xx ++ 19x19x -- 21621666 33

55 pp++ 22(( )) (( ))33

== pp ++ 33 ⋅⋅ pp ⋅⋅ 22 ++ 33 ⋅⋅ pp ⋅⋅ 22 ++ 2233 22 22 33

== pp ++ 6p6p ++ 12p12p++ 8833 22

66 aa -- 33 ((aa ++ 3a3a++ 99 == aa -- 27 27 (( )) (( )) 22 )) 33

77 aa -- bb -- cc ((aa++ bb -- cc(( )) (( )) ))== aa -- cc -- bb aa -- cc++ bb(( ))(( ))

== aa -- cc -- bb(( ))22 22

== aa -- bb ++ cc -- 2ac2ac22 22 22

88 ((aa ++ 2a2a -- 33 ((aa -- 2a2a++ 33(( )) 22 )) 22 ))

== ((aa ++ 2a2a -- 33 aa -- 2a2a -- 33 }}22 )){{ 22 (( ))

== aa -- 2a2a -- 3344 (( ))22

== aa -- ((4a4a -- 12a12a++ 9944 22 ))

== aa -- 4a4a ++ 12a12a -- 9944 22

99 xx -- 2y2y(( )) (( ))33

== xx -- 33 ⋅⋅ xx ⋅⋅ 2y2y++ 33 ⋅⋅ xx ⋅⋅ 2y2y -- 2y2y33 22 (( ))22 (( ))33

== xx -- 6x6x yy++ 12xy12xy -- 8y8y33 22 22 33

1010 xx++ yy++ zz(( )) (( ))22

== xx++ yy ++ 22 xx++ yy zz++ zz(( ))22 (( )) 22

== xx ++ 2xy2xy++ yy ++ 2xz2xz++ 2yz2yz++ zz22 22 22

== xx ++ yy ++ zz ++ 2xy2xy++ 2yz2yz++ 2zx2zx22 22 22

1111 ((xx -- 11 ((xx ++ 22 ((xx ++ 11))((xx -- 22))(( )) 22 )) 22 )) 22 22

== ((xx -- 11 ((xx ++ 11))((xx ++ 22 ((xx -- 22))22 )) 22 22 )) 22

== ((xx -- 11 ((xx -- 4444 )) 44 ))

== xx -- 5x5x ++ 4488 44

1212 3q3q++ 2r2r 3q3q -- 2r2r(( )) (( ))22(( ))22

== 3q3q++ 2r2r 3q3q -- 2r2r }}{{(( ))(( )) 22

== 9q9q -- 4r4r }}{{ 22 22 22

== 81q81q -- 72q72q rr ++ 16r16r44 22 22 44




11 xx++ 2y2y -- zz(( )) (( ))22 22 ((aa ++ 2a2a -- 33 ((aa -- 2a2a++ 33(( )) 22 )) 22 ))

33 aa -- 2b2b ((aa ++ 2ab2ab++ 4b4b(( )) (( )) 22 22)) 44 2a2a++ bb++ cc 2a2a -- bb -- cc(( )) (( ))(( ))

55 aa++ 44 ((aa -- 4a4a++ 1616(( )) (( )) 22 )) 66 aa++ 3b3b aa -- 3b3b(( )) (( ))22(( ))22

77 pp -- 33(( )) (( ))33 88 xx++ 22 ((xx -- 11 xx++ 33 ((xx++ 66(( )) (( )) ))(( )) ))

99 ((xx ++ 33 ((xx ++ 22 ((xx -- 33))((xx -- 22))(( )) 22 )) 22 )) 22 22 1010 xx -- 11 ((xx -- xx++ 11)) xx++ 11 ((xx ++ xx++ 11(( )) (( )) 22 (( )) 22 ))

1111 2x2x++ yy -- zz ((2x2x -- yy++ zz(( )) (( )) )) 1212 2x2x++ yy(( )) (( ))33




11 xx++ 2y2y -- zz(( )) (( ))22

== xx++ 2y2y -- 22 xx++ 2y2y zz++ zz(( ))22 (( )) 22

== xx ++ 4xy4xy++ 4y4y -- 2xz2xz -- 4yz4yz++ zz22 22 22

== xx ++ 4y4y ++ zz ++ 4xy4xy -- 4yz4yz -- 2zx2zx22 22 22

22 ((aa ++ 2a2a -- 33 ((aa -- 2a2a++ 33(( )) 22 )) 22 ))

== {{aa ++ 2a2a -- 33 }}{{aa -- 2a2a -- 33 }}22 (( )) 22 (( ))

== aa -- 2a2a -- 3344 (( ))22

== aa -- 4a4a ++ 12a12a -- 9944 22

33 aa -- 2b2b ((aa ++ 2ab2ab++ 4b4b == aa -- 8b8b(( )) (( )) 22 22)) 33 33 44 2a2a++ bb++ cc 2a2a -- bb -- cc(( )) (( ))(( ))== {{2a2a++ bb++ cc }}{{2a2a -- bb++ cc }}(( )) (( ))

== 4a4a -- bb++ cc22 (( ))22

== 4a 4a -- bb -- cc -- 2bc2bc22 22 22

55 aa++ 44 ((aa -- 4a4a++ 1616 == aa ++ 6464(( )) (( )) 22 )) 33 66 aa++ 3b3b aa -- 3b3b(( )) (( ))22(( ))22

== {{ aa++ 3b3b aa -- 3b3b }}(( ))(( )) 22

== ((aa -- 9b9b22 22))22

== aa -- 18a18a bb ++ 81b81b44 22 22 44

77 pp -- 33(( )) (( ))33

== pp ++ 33 ⋅⋅ pp ⋅⋅ --33 ++ 33 ⋅⋅ pp ⋅⋅ --33 -- 3333 22 (( )) (( ))22 33

== pp -- 9p9p ++ 27p27p -- 272733 22

88 xx++ 22 ((xx -- 11 xx++ 33 ((xx++ 66(( )) (( )) ))(( )) ))== xx++ 22 xx++ 33 ((xx -- 11 ((xx++ 66(( ))(( )) )) ))

== ((xx ++ 5x5x++ 66 ((xx ++ 5x5x -- 6622 )) 22 ))

== ((xx ++ 5x5x -- 363622 ))22

== xx ++ 10x10x ++ 25x25x -- 363644 33 22

99 ((xx ++ 33 ((xx ++ 22 ((xx -- 33))((xx -- 22))(( )) 22 )) 22 )) 22 22

== ((xx ++ 33 ((xx -- 33))((xx ++ 22 ((xx -- 22))22 )) 22 22 )) 22

== ((xx -- 99 ((xx -- 4444 )) 44 ))

== xx -- 13x13x ++ 363688 44

1010 xx -- 11 ((xx -- xx++ 11)) xx++ 11 ((xx ++ xx++ 11(( )) (( )) 22 (( )) 22 ))

== xx -- 11 ((xx ++ xx++ 11 xx++ 11 ((xx -- xx++ 11))(( )) 22 ))(( )) 22

== ((xx -- 11 ((xx ++ 1133 )) 33 ))

== xx -- 1166

1111 2x2x++ yy -- zz ((2x2x -- yy -- zz(( )) (( )) ))== 2x2x -- zz++ yy ((2x2x -- zz -- yy(( )) ))

== 2x2x -- zz -- yy(( ))22 22

== 4x4x -- yy ++ zz -- 4xz4xz22 22 22

1212 2x2x++ yy(( )) (( ))33

== 2x2x ++ 33 ⋅⋅ ((2x2x ⋅⋅ yy++ 33 ⋅⋅ 2x2x ⋅⋅ yy ++ yy(( ))33 ))22 22 33

== 8x8x ++ 12x12x yy++ 6xy6xy ++ yy33 22 22 33




11 xx -- 11 ((xx -- 33 xx -- 55 ((xx -- 77(( )) (( )) ))(( )) )) 22 aa -- bb -- cc(( )) (( ))22

33 3x3x -- yy ((9x9x ++ 3xy3xy++ yy(( )) (( )) 22 22)) 44 2x2x -- 11(( )) (( ))33

55 aa++ bb aa -- bb ((aa -- 3b3b(( )) (( ))(( ))22 )) 66 xx -- 33 xx++ 33(( )) (( ))22(( ))22

77 ((aa -- 2a2a -- 33 ((aa ++ 2a2a -- 33(( )) 22 )) 22 )) 88 ((xx -- 2x2x++ 44)) xx -- 22 xx++ 22 ((xx ++ 2x2x++ 44(( )) 22 (( ))(( )) 22 ))

99 ((2a2a -- 11 ((2a2a ++ 33 ((2a2a ++ 11))((2a2a -- 33))(( )) 22 )) 22 )) 22 22 1010 ((xx ++ yy -- 11 ((xx -- yy ++ 11(( )) 22 22 )) 22 22 ))

1111 2a2a++ 3b3b(( )) (( ))33 1212 2x2x++ 33 ((4x4x -- 6x6x++ 99(( )) (( )) 22 ))




11 xx -- 11 ((xx -- 33 xx -- 55 ((xx -- 77(( )) (( )) ))(( )) ))== xx -- 11 ((xx -- 77 ((xx -- 33 xx -- 55(( )) )) ))(( ))

== ((xx -- 8x8x++ 77 ((xx -- 8x8x++ 151522 )) 22 ))

== ((xx -- 8x8x ++ 2222((xx -- 8x8x ++ 10510522 ))22 22 ))

== xx -- 16x16x ++ 64x64x ++ 22x22x -- 176x176x++ 10510544 33 22 22

== xx -- 16x16x ++ 86x86x -- 176x176x++ 10510544 33 22

22 aa -- bb -- cc(( )) (( ))22

== aa -- bb -- 2c2c aa -- bb ++ cc(( ))22 (( )) 22

== aa -- 2ab2ab++ bb -- 2ca2ca++ 2bc2bc++ cc22 22 22

== aa ++ bb ++ cc -- 2ab2ab++ 2bc2bc -- 2ca2ca22 22 22

33 3x3x -- yy ((9x9x ++ 3xy3xy++ yy == 27x27x -- yy(( )) (( )) 22 22)) 33 33 44 2x2x -- 11(( )) (( ))33

== ((2x2x -- 33 ⋅⋅ ((2x2x ⋅⋅ 11 ++ 33 ⋅⋅ 2x2x ⋅⋅ 11-- 11))22 ))22 33

== 8x8x -- 12x12x ++ 6x6x -- 1122 22

55 aa++ bb aa -- bb ((aa -- 3b3b(( )) (( ))(( ))22 ))

== aa++ bb ((aa -- 3b3b aa -- bb(( )) ))(( ))22

== ((aa -- 2ab2ab -- 3b3b ((aa -- 2ab2ab++ bb22 22)) 22 22))

== ((aa -- 2ab2ab -- 2b2b ((aa -- 2ab2ab -- 3b3b22 ))22 22 22 )) 44

== aa -- 4a4a bb++ 4a4a bb -- 2a2a bb ++ 4ab4ab -- 3b3b44 33 22 22 22 22 33 44

== aa -- 4a4a bb++ 2a2a bb ++ 4ab4ab -- 3b3b44 33 22 22 33 44

66 xx -- 33 xx++ 33(( )) (( ))22(( ))22

== xx -- 33 xx++ 33{{(( ))(( ))}}22

== ((xx -- 9922 ))22

== xx -- 18x18x ++ 818144 22

77 ((aa -- 2a2a -- 33 ((aa ++ 2a2a -- 33(( )) 22 )) 22 ))

== ((aa -- 33-- 2a2a ((aa -- 33 ++ 2a2a22 )) 22 ))

== ((aa -- 33 -- 4a4a22 ))22 22

== aa -- 6a6a ++ 99-- 4a4a44 22 22

== aa -- 10a10a ++ 9944 22

88 ((xx -- 2x2x++ 44)) xx -- 22 xx++ 22 ((xx ++ 2x2x++ 44(( )) 22 (( ))(( )) 22 ))

== xx++ 22 ((xx -- 2x2x++ 44)) xx -- 22 ((xx ++ 2x2x++ 44(( )) 22 (( )) 22 ))

== ((xx ++ 88 ((xx -- 8833 )) 33 ))

== xx -- 646466

99 ((2a2a -- 11 ((2a2a ++ 33 ((2a2a ++ 11))((2a2a -- 33))(( )) 22 )) 22 )) 22 22

== ((2a2a -- 11 ((2a2a ++ 11))((2a2a ++ 33 ((2a2a -- 33))22 )) 22 22 )) 22

== ((4a4a -- 11 ((4a4a -- 9944 )) 44 ))

== 16a16a -- 40a40a ++ 9988 44

1010 ((xx ++ yy -- 11 ((xx -- yy ++ 11(( )) 22 22 )) 22 22 ))

== xx ++ ((yy -- 11)) xx -- ((yy -- 11))22 22 22 22

== xx -- ((yy -- 1144 22 ))22

== xx -- yy ++ 2y2y -- 1144 44 22

1111 2a2a++ 3b3b(( )) (( ))33

== ((2a2a ++ 33 ⋅⋅ ((2a2a ⋅⋅ 3b3b++ 33 ⋅⋅ 2a2a ⋅⋅ ((3b3b ++ ((3b3b))33 ))22 ))22 ))33

== 8a8a ++ 36a36a bb++ 54ab54ab ++ 27b27b33 22 22 33

1212 2x2x++ 33 ((4x4x -- 6x6x++ 99 == 8x8x ++ 2727(( )) (( )) 22 )) 33

