忙しい人のための中学数学【式の展開の解答／中編】

　こちらのnoteの解答編です。

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乗法の公式①【その1】・・・計60問

A（20問）

① (x+1)(x+2)
=x²+3x+2

② (x+2)(x+3)
=x²+5x+6

③ (x+3)(x+4)
=x²+7x+12

④ (x+4)(x+5)
=x²+9x+20

⑤ (x+5)(x+6)
=x²+11x+30

⑥ (x+6)(x+7)
=x²+13x+42

⑦ (x+7)(x+8)
=x²+15x+56

⑧ (x+8)(x+9)
=x²+17x+72

⑨ (x+9)(x+10)
=x²+19x+90

⑩ (x+1)(x+3)
=x²+4x+3

⑪ (x+2)(x+4)
=x²+6x+8

⑫ (x+3)(x+5)
=x²+8x+15

⑬ (x+4)(x+6)
=x²+10x+24

⑭ (x+5)(x+7)
=x²+12x+35

⑮ (x+6)(x+8)
=x²+14x+48

⑯ (x+7)(x+9)
=x²+16x+63

⑰ (x+8)(x+10)
=x²+18x+80

⑱ (x+9)(x+11)
=x²+20x+99

⑲ (x+1)(x+4)
=x²+5x+4

⑳ (x+2)(x+5)
=x²+7x+10

B（20問）

① (x+3)(x+6)
=x²+9x+18

② (x+4)(x+7)
=x²+11x+28

③ (x+5)(x+8)
=x²+13x+40

④ (x+6)(x+9)
=x²+15x+54

⑤ (x+7)(x+10)
=x²+17x+70

⑥ (x+8)(x+11)
=x²+19x+88

⑦ (x+9)(x+12)
=x²+21x+108

⑧ (x+1)(x+5)
=x²+6x+5

⑨ (x+2)(x+6)
=x²+8x+12

⑩ (x+3)(x+7)
=x²+10x+21

⑪ (x+4)(x+8)
=x²+12x+32

⑫ (x+5)(x+9)
=x²+14x+45

⑬ (x+6)(x+10)
=x²+16x+60

⑭ (x+7)(x+11)
=x²+18x+77

⑮ (x+8)(x+12)
=x²+20x+96

⑯ (x+9)(x+13)
=x²+22x+117

⑰ (x+1)(x+6)
=x²+7x+6

⑱ (x+2)(x+7)
=x²+9x+14

⑲ (x+3)(x+8)
=x²+11x+24

⑳ (x+4)(x+9)
=x²+13x+36

C（20問）

① (x+5)(x+10)
=x²+15x+50

② (x+6)(x+11)
=x²+17x+66

③ (x+7)(x+12)
=x²+19x+84

④ (x+8)(x+13)
=x²+21x+104

⑤ (x+9)(x+14)
=x²+23x+126

⑥ (x+1)(x+7)
=x²+8x+7

⑦ (x+2)(x+8)
=x²+10x+16

⑧ (x+3)(x+9)
=x²+12x+27

⑨ (x+4)(x+10)
=x²+14x+40

⑩ (x+5)(x+11)
=x²+16x+55

⑪ (x+6)(x+12)
=x²+18x+72

⑫ (x+7)(x+13)
=x²+20x+91

⑬ (x+8)(x+14)
=x²+22x+112

⑭ (x+9)(x+15)
=x²+24x+135

⑮ (x+1)(x+8)
=x²+9x+8

⑯ (x+2)(x+9)
=x²+11x+18

⑰ (x+3)(x+10)
=x²+13x+30

⑱ (x+4)(x+11)
=x²+15x+44

⑲ (x+5)(x+12)
=x²+17x+60

⑳ (x+6)(x+13)
=x²+19x+78

乗法の公式①【その2】・・・計60問

A（20問）

① (x−1)(x−2)
=x²−3x+2

② (x−2)(x−3)
=x²−5x+6

③ (x−3)(x−4)
=x²−7x+12

④ (x−4)(x−5)
=x²−9x+20

⑤ (x−5)(x−6)
=x²−11x+30

⑥ (x−6)(x−7)
=x²−13x+42

⑦ (x−7)(x−8)
=x²−15x+56

⑧ (x−8)(x−9)
=x²−17x+72

⑨ (x−9)(x−10)
=x²−19x+90

⑩ (x−1)(x−3)
=x²−4x+3

⑪ (x−2)(x−4)
=x²−6x+8

⑫ (x−3)(x−5)
=x²−8x+15

⑬ (x−4)(x−6)
=x²−10x+24

⑭ (x−5)(x−7)
=x²−12x+35

⑮ (x−6)(x−8)
=x²−14x+42

⑯ (x−7)(x−9)
=x²−16x+63

⑰ (x−8)(x−10)
=x²−18x+80

⑱ (x−9)(x−11)
=x²−20x+99

⑲ (x−1)(x−4)
=x²−5x+4

⑳ (x−2)(x−5)
=x²−7x+10

B（20問）

① (x−3)(x−6)
=x²−9x+18

② (x−4)(x−7)
=x²−11x+28

③ (x−5)(x−8)
=x²−13x+40

④ (x−6)(x−9)
=x²−15x+54

⑤ (x−7)(x−10)
=x²−17x+70

⑥ (x−8)(x−11)
=x²−19x+88

⑦ (x−9)(x−12)
=x²−21x+108

⑧ (x−1)(x−5)
=x²−6x+5

⑨ (x−2)(x−6)
=x²−8x+12

⑩ (x−3)(x−7)
=x²−10x+21

⑪ (x−4)(x−8)
=x²−12x+32

⑫ (x−5)(x−9)
=x²−14x+45

⑬ (x−6)(x−10)
=x²−16x+60

⑭ (x−7)(x−11)
=x²−18x+77

⑮ (x−8)(x−12)
=x²−20x+96

⑯ (x−9)(x−13)
=x²−22x+117

⑰ (x−1)(x−6)
=x²−7x+6

⑱ (x−2)(x−7)
=x²−9x+14

⑲ (x−3)(x−8)
=x²−11x+24

⑳ (x−4)(x−9)
=x²−13x+36

C（20問）

① (x−5)(x−10)
=x²−15x+50

② (x−6)(x−11)
=x²−17x+66

③ (x−7)(x−12)
=x²−19x+84

④ (x−8)(x−13)
=x²−21x+104

⑤ (x−9)(x−14)
=x²−23x+126

⑥ (x−1)(x−7)
=x²−8x+7

⑦ (x−2)(x−8)
=x²−10x+16

⑧ (x−3)(x−9)
=x²−12x+27

⑨ (x−4)(x−10)
=x²−14x+40

⑩ (x−5)(x−11)
=x²−16x+55

⑪ (x−6)(x−12)
=x²−18x+72

⑫ (x−7)(x−13)
=x²−20x+91

⑬ (x−8)(x−14)
=x²−22x+112

⑭ (x−9)(x−15)
=x²−24x+135

⑮ (x−1)(x−8)
=x²−9x+8

⑯ (x−2)(x−9)
=x²−11x+18

⑰ (x−3)(x−10)
=x²−13x+30

⑱ (x−4)(x−11)
=x²−15x+44

⑲ (x−5)(x−12)
=x²−17x+60

⑳ (x−6)(x−13)
=x²−19x+78

乗法の公式①【その3】・・・計60問

A（20問）

① (x+1)(x−2)
=x²−x−2

② (x+2)(x−3)
=x²−x−6

③ (x+3)(x−4)
=x²−x−12

④ (x+4)(x−5)
=x²−x−20

⑤ (x+5)(x−6)
=x²−x−30

⑥ (x+6)(x−7)
=x²−x−42

⑦ (x+7)(x−8)
=x²−x−56

⑧ (x+8)(x−9)
=x²−x−72

⑨ (x+9)(x−10)
=x²−x−90

⑩ (x+1)(x−3)
=x²−2x−3

⑪ (x+2)(x−4)
=x²−2x−8

⑫ (x+3)(x−5)
=x²−2x−15

⑬ (x+4)(x−6)
=x²−2x−24

⑭ (x+5)(x−7)
=x²−2x−35

⑮ (x+6)(x−8)
=x²−2x−48

⑯ (x+7)(x−9)
=x²−2x−63

⑰ (x+8)(x−10)
=x²−2x−80

⑱ (x+9)(x−11)
=x²−2x−99

⑲ (x+1)(x−4)
=x²−3x−4

⑳ (x+2)(x−5)
=x²−3x−10

B（20問）

① (x+3)(x−6)
=x²−3x−18

② (x+4)(x−7)
=x²−3x−28

③ (x+5)(x−8)
=x²−3x−40

④ (x+6)(x−9)
=x²−3x−54

⑤ (x+7)(x−10)
=x²−3x−70

⑥ (x+8)(x−11)
=x²−3x−88

⑦ (x+9)(x−12)
=x²−3x−108

⑧ (x+1)(x−5)
=x²−4x−5

⑨ (x+2)(x−6)
=x²−4x−12

⑩ (x+3)(x−7)
=x²−4x−21

⑪ (x+4)(x−8)
=x²−4x−32

⑫ (x+5)(x−9)
=x²−4x−45

⑬ (x+6)(x−10)
=x²−4x−60

⑭ (x+7)(x−11)
=x²−4x−77

⑮ (x+8)(x−12)
=x²−4x−96

⑯ (x+9)(x−13)
=x²−4x−117

⑰ (x+1)(x−6)
=x²−5x−6

⑱ (x+2)(x−7)
=x²−5x−14

⑲ (x+3)(x−8)
=x²−5x−24

⑳ (x+4)(x−9)
=x²−5x−36

C（20問）

① (x+5)(x−10)
=x²−5x−50

② (x+6)(x−11)
=x²−5x−66

③ (x+7)(x−12)
=x²−5x−84

④ (x+8)(x−13)
=x²−5x−104

⑤ (x+9)(x−14)
=x²−5x−126

⑥ (x+1)(x−7)
=x²−6x−7

⑦ (x+2)(x−8)
=x²−6x−16

⑧ (x+3)(x−9)
=x²−6x−27

⑨ (x+4)(x−10)
=x²−6x−40

⑩ (x+5)(x−11)
=x²−6x−55

⑪ (x+6)(x−12)
=x²−6x−72

⑫ (x+7)(x−13)
=x²−6x−91

⑬ (x+8)(x−14)
=x²−6x−112

⑭ (x+9)(x−15)
=x²−6x−135

⑮ (x+1)(x−8)
=x²−7x−8

⑯ (x+2)(x−9)
=x²−7x−18

⑰ (x+3)(x−10)
=x²−7x−30

⑱ (x+4)(x−11)
=x²−7x−44

⑲ (x+5)(x−12)
=x²−7x−60

⑳ (x+6)(x−13)
=x²−7x−78

乗法の公式①【その4】・・・計60問

A（20問）

① (x−1)(x+2)
=x²+x−2

② (x−2)(x+3)
=x²+x−6

③ (x−3)(x+4)
=x²+x−12

④ (x−4)(x+5)
=x²+x−20

⑤ (x−5)(x+6)
=x²+x−30

⑥ (x−6)(x+7)
=x²+x−42

⑦ (x−7)(x+8)
=x²+x−56

⑧ (x−8)(x+9)
=x²+x−72

⑨ (x−9)(x+10)
=x²+x−90

⑩ (x−1)(x+3)
=x²+2x−3

⑪ (x−2)(x+4)
=x²+2x−8

⑫ (x−3)(x+5)
=x²+2x−15

⑬ (x−4)(x+6)
=x²+2x−24

⑭ (x−5)(x+7)
=x²+2x−35

⑮ (x−6)(x+8)
=x²+2x−48

⑯ (x−7)(x+9)
=x²+2x−63

⑰ (x−8)(x+10)
=x²+2x−80

⑱ (x−9)(x+11)
=x²+2x−99

⑲ (x−1)(x+4)
=x²+3x−4

⑳ (x−2)(x+5)
=x²+3x−10

B（20問）

① (x−3)(x+6)
=x²+3x−18

② (x−4)(x+7)
=x²+3x−28

③ (x−5)(x+8)
=x²+3x−40

④ (x−6)(x+9)
=x²+3x−54

⑤ (x−7)(x+10)
=x²+3x−70

⑥ (x−8)(x+11)
=x²+3x−88

⑦ (x−9)(x+12)
=x²+3x−108

⑧ (x−1)(x+5)
=x²+4x−5

⑨ (x−2)(x+6)
=x²+4x−12

⑩ (x−3)(x+7)
=x²+4x−21

⑪ (x−4)(x+8)
=x²+4x−32

⑫ (x−5)(x+9)
=x²+4x−45

⑬ (x−6)(x+10)
=x²+4x−60

⑭ (x−7)(x+11)
=x²+4x−77

⑮ (x−8)(x+12)
=x²+4x−96

⑯ (x−9)(x+13)
=x²+4x−117

⑰ (x−1)(x+6)
=x²+5x−6

⑱ (x−2)(x+7)
=x²+5x−14

⑲ (x−3)(x+8)
=x²+5x−24

⑳ (x−4)(x+9)
=x²+5x−36

C（20問）

① (x−5)(x+10)
=x²+5x−50

② (x−6)(x+11)
=x²+5x−66

③ (x−7)(x+12)
=x²+5x−84

④ (x−8)(x+13)
=x²+5x−104

⑤ (x−9)(x+14)
=x²+5x−126

⑥ (x−1)(x+7)
=x²+6x−7

⑦ (x−2)(x+8)
=x²+6x−16

⑧ (x−3)(x+9)
=x²+6x−27

⑨ (x−4)(x+10)
=x²+6x−40

⑩ (x−5)(x+11)
=x²+6x−55

⑪ (x−6)(x+12)
=x²+6x−72

⑫ (x−7)(x+13)
=x²+6x−91

⑬ (x−8)(x+14)
=x²+6x−112

⑭ (x−9)(x+15)
=x²+6x−135

⑮ (x−1)(x+8)
=x²+7x−8

⑯ (x−2)(x+9)
=x²+7x−18

⑰ (x−3)(x+10)
=x²+7x−30

⑱ (x−4)(x+11)
=x²+7x−44

⑲ (x−5)(x+12)
=x²+7x−60

⑳ (x−6)(x+13)
=x²+7x−78

乗法の公式②・・・計40問

A（20問）

① (x+1)²
=x²+2x+1

② (x+2)²
=x²+4x+4

③ (x+3)²
=x²+6x+9

④ (x+4)²
=x²+8x+16

⑤ (x+5)²
=x²+10x+25

⑥ (x+6)²
=x²+12x+36

⑦ (x+7)²
=x²+14x+49

⑧ (x+8)²
=x²+16x+64

⑨ (x+9)²
=x²+18x+81

⑩ (x+10)²
=x²+20x+100

⑪ (x+11)²
=x²+22x+121

⑫ (x+12)²
=x²+24x+144

⑬ (x+13)²
=x²+26x+169

⑭ (x+14)²
=x²+28x+196

⑮ (x+15)²
=x²+30x+225

⑯ (2x+y)²
=(2x)²+2×2x×y+y²
=4x²+4xy+y²

⑰ (3x+2y)²
=(3x)²+2×3x×2y+(2y)²
=9x²+12xy+4y²

⑱ (4x+3y)²
=(4x)²+2×4x×3y+(3y)²
=16x²+24xy+9y²

⑲ (5x+4y)²
=(5x)²+2×5x×4y+(4y)²
=25x²+40xy+16y²

⑳ (6x+5y)²
=(6x)²+2×6x×5y+(5y)²
=36x²+60xy+25y²

B（20問）

① (7x+6y)²
=(7x)²+2×7x×6y+(6y)²
=49x²+84xy+36y²

② (8x+7y)²
=(8x)²+2×8x×7y+(7y)²
=64x²+112xy+49y²

③ (9x+8y)²
=(9x)²+2×9x×8y+(8y)²
=81x²+144xy+64y²

④ (10x+9y)²
=(10x)²+2×10x×9y+(9y)²
=100x²+180xy+81y²

⑤ (11x+10y)²
=(11x)²+2×11x×10y+(10y)²
=121x²+220xy+100y²

⑥ (12x+11y)²
=(12x)²+2×12x×11y+(11y)²
=144x²+264xy+121y²

⑦ (13x+12y)²
=(13x)²+2×13x×12y+(12y)²
=169x²+312xy+144y²

⑧ (14x+13y)²
=(14x)²+2×14x×13y+(13y)²
=196x²+364xy+169y²

⑨ (15x+14y)²
=(15x)²+2×15x×14y+(14y)²
=225x²+420xy+196y²

⑩ (−x+2y)²
=(−x)²+2×(−x)×2y+(2y)²
=x²−4xy+4y²

⑪ (−2x+3y)²
=(−2x)²+2×(−2x)×3y+(3y)²
=4x²−12xy+9y²

⑫ (−3x+4y)²
=(−3x)²+2×(−3x)×4y+(4y)²
=9x²−24xy+16y²

⑬ (−4x+5y)²
=(−4x)²+2×(−4x)×5y+(5y)²
=16x²−40xy+25y²

⑭ (−5x+6y)²
=(−5x)²+2×(−5x)×6y+(6y)²
=25x²−60xy+36y²

⑮ (−6x+7y)²
=(−6x)²+2×(−6x)×7y+(7y)²
=36x²−84xy+49y²

⑯ (−7x+8y)²
=(−7x)²+2×(−7x)×8y+(8y)²
=49x²−112xy+64y²

⑰ (−8x+9y)²
=(−8x)²+2×(−8x)×9y+(9y)²
=64x²−144xy+81y²

⑱ (−9x+10y)²
=(−9x)²+2×(−9x)×10y+(10y)²
=81x²−180xy+100y²

⑲ (−10x+11y)²
=(−10x)²+2×(−10x)×11y+(11y)²
=100x²−220xy+121y²

⑳ (−11x+12y)²
=(−11x)²+2×(−11x)×12y+(12y)²
=121x²−264xy+144y²

乗法の公式③・・・計40問

A（20問）

① (x−1)²
=x²−2x+1

② (x−2)²
=x²−4x+4

③ (x−3)²
=x²−6x+9

④ (x−4)²
=x²−8x+16

⑤ (x−5)²
=x²−10x+25

⑥ (x−6)²
=x²−12x+36

⑦ (x−7)²
=x²−14x+49

⑧ (x−8)²
=x²−16x+64

⑨ (x−9)²
=x²−18x+81

⑩ (x−10)²
=x²−20x+100

⑪ (x−11)²
=x²−22x+121

⑫ (x−12)²
=x²−24x+144

⑬ (x−13)²
=x²−26x+169

⑭ (x−14)²
=x²−28x+196

⑮ (x−15)²
=x²−30x+225

⑯ (2x−y)²
=(2x)²−2×2x×y+y²
=4x²−4xy+y²

⑰ (3x−2y)²
=(3x)²−2×3x×2y+(2y)²
=9x²−12xy+4y²

⑱ (4x−3y)²
=(4x)²−2×4x×3y+(3y)²
=16x²−24xy+9y²

⑲ (5x−4y)²
=(5x)²−2×5x×4y+(4y)²
=25x²−40xy+16y²

⑳ (6x−5y)²
=(6x)²−2×6x×5y+(5y)²
=36x²−60xy+25y²

B（20問）

① (7x−6y)²
=(7x)²−2×7x×6y+(6y)²
=49x²−84xy+36y²

② (8x−7y)²
=(8x)²−2×8x×7y+(7y)²
=64x²−112xy+49y²

③ (9x−8y)²
=(9x)²−2×9x×8y+(8y)²
=81x²−144xy+64y²

④ (10x−9y)²
=(10x)²−2×10x×9y+(9y)²
=100x²−180xy+81y²

⑤ (11x−10y)²
=(11x)²−2×11x×10y+(10y)²
=121x²−220xy+100y²

⑥ (12x−11y)²
=(12x)²−2×12x×11y+(11y)²
=144x²−264xy+121y²

⑦ (13x−12y)²
=(13x)²−2×13x×12y+(12y)²
=169x²−312xy+144y²

⑧ (14x−13y)²
=(14x)²−2×14x×13y+(13y)²
=196x²−364xy+169y²

⑨ (15x−14y)²
=(15x)²−2×15x×14y+(14y)²
=225x²−420xy+196y²

⑩ (−x−2y)²
=(−x)²−2×(−x)×2y+(2y)²
=x²+4xy+4y²

⑪ (−2x−3y)²
=(−2x)²−2×(−2x)×3y+(3y)²
=4x²+12xy+9y²

⑫ (−3x−4y)²
=(−3x)²−2×(−3x)×4y+(4y)²
=9x²+24xy+16y²

⑬ (−4x−5y)²
=(−4x)²−2×(−4x)×5y+(5y)²
=16x²+40xy+25y²

⑭ (−5x−6y)²
=(−5x)²−2×(−5x)×6y+(6y)²
=25x²+60xy+36y²

⑮ (−6x−7y)²
=(−6x)²−2×(−6x)×7y+(7y)²
=36x²+84xy+49y²

⑯ (−7x−8y)²
=(−7x)²−2×(−7x)×8y+(8y)²
=49x²+112xy+64y²

⑰ (−8x−9y)²
=(−8x)²−2×(−8x)×9y+(9y)²
=64x²+144xy+81y²

⑱ (−9x−10y)²
=(−9x)²−2×(−9x)×10y+(10y)²
=81x²+180xy+100y²

⑲ (−10x−11y)²
=(−10x)²−2×(−10x)×11y+(11y)²
=100x²+220xy+121y²

⑳ (−11x−12y)²
=(−11x)²−2×(−11x)×12y+(12y)²
=121x²+264xy+144y²

乗法の公式④・・・計40問

A（20問）

① (x+1)(x−1)
=x²−1

② (x+2)(x−2)
=x²−4

③ (x+3)(x−3)
=x²−9

④ (x+4)(x−4)
=x²−16

⑤ (x+5)(x−5)
=x²−25

⑥ (x+6)(x−6)
=x²−36

⑦ (x+7)(x−7)
=x²−49

⑧ (x+8)(x−8)
=x²−64

⑨ (x+9)(x−9)
=x²−81

⑩ (x+10)(x−10)
=x²−100

⑪ (x+11)(x−11)
=x²−121

⑫ (x+12)(x−12)
=x²−144

⑬ (x+13)(x−13)
=x²−169

⑭ (x+14)(x−14)
=x²−196

⑮ (x+15)(x−15)
=x²−225

⑯ (2x+y)(2x−y)
=4x²−y²

⑰ (3x+2y)(3x−2y)
=9x²−4y²

⑱ (4x+3y)(4x−3y)
=16x²−9y²

⑲ (5x+4y)(5x−4y)
=25x²−16y²

⑳ (6x+5y)(6x−5y)
=36x²−25y²

B（20問）

① (7x+6y)(7x−6y)
=49x²−36y²

② (8x+7y)(8x−7y)
=64x²−49y²

③ (9x+8y)(9x−8y)
=81x²−64y²

④ (10x+9y)(10x−9y)
=100x²−81y²

⑤ (11x+10y)(11x−10y)
=121x²−100y²

⑥ (12x+11y)(12x−11y)
=144x²−121y²

⑦ (13x+12y)(13x−12y)
=169x²−144y²

⑧ (14x+13y)(14x−13y)
=196x²−169y²

⑨ (15x+14y)(15x−14y)
=225x²−196y²

⑩ (−a+b)(a+b)
=(b−a)(b+a)
=b²−a²

⑪ (−3a+b)(3a+b)
=(b−3a)(b+3a)
=b²−9a²

⑫ (−5a+b)(5a+b)
=(b−5a)(b+5a)
=b²−25a²

⑬ (−7a+b)(7a+b)
=(b−7a)(b+7a)
=b²−49a²

⑭ (−9a+b)(9a+b)
=(b−9a)(b+9a)
=b²−81a²

⑮ (2+t)(2−t)
=4−t²

⑯ (4+3t)(4−3t)
=16−9t²

⑰ (6+5t)(6−5t)
=36−25t²

⑱ (8+7t)(8−7t)
=64−49t²

⑲ (10+9t)(10−9t)
=100−81t²

⑳ (12+11t)(12−11t)
=144−121t²