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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

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  • 展開 No.2展開 No.2 次の式を展開しなさい。次の式を展開しなさい。

    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

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  • 展開 No.2(解答)展開 No.2(解答)

    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

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  • 展開 No.3展開 No.3 次の式を展開しなさい。次の式を展開しなさい。

    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

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  • 展開 No.3(解答)展開 No.3(解答)

    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