忙しい人のための中学数学【因数分解の解答／前編】

　「素因数分解」と「共通因数をとり出す」タイプの問題、解答編です。

　問題編はこちら↓

その他の単元や計算問題は、リンク集からどうぞ↓

素因数分解・・・計20問

①20
= 2²×5

②30
= 2×3×5

③40
= 2³×5

④50
= 2×5²

⑤60
= 2²×3×5

⑥70
= 2×5×7

⑦80
= 2⁴×5

⑧90
= 2×3²×5

⑨100
= 2²×5²

⑩120
= 2³×3×5

⑪140
= 2²×5×7

⑫160
= 2⁵×5

⑬180
= 2²×3²×5

⑭200
= 2³×5²

⑮240
= 2⁴×3×5

⑯280
= 2³×5×7

⑰320
= 2⁶×5

⑱360
= 2³×3²×5

⑲400
= 2⁴×5²

⑳450
= 2×3²×5²

共通因数をとり出す・・・計80問

A（20問）

① 2x²+3xy
= x(2x+3y)

② 6x²+8xy
= 2x(3x+4y)

③ 12x²+15xy
= 3x(4x+5y)

④ 20x²+24xy
= 4x(5x+6y)

⑤ 30x²+35xy
= 5x(6x+7y)

⑥ 42x²+48xy
= 6x(7x+8y)

⑦ 56x²+63xy
= 7x(8x+9y)

⑧ 72x²+80xy
= 8x(9x+10y)

⑨ 90x²+99xy
= 9x(10x+11y)

⑩ 110x²+120xy
= 10x(11x+12y)

⑪ 2a²+2ab
= 2a(a+b)

⑫ 6a²+6ab
= 6a(a+b)

⑬ 12a²+12ab
= 12a(a+b)

⑭ 20a²+20ab
= 20a(a+b)

⑮ 30a²+30ab
= 30a(a+b)

⑯ 42a²+42ab
= 42a(a+b)

⑰ 56a²+56ab
= 56a(a+b)

⑱ 72a²+72ab
= 72a(a+b)

⑲ 90a²+90ab
= 90a(a+b)

⑳ 110a²+110ab
= 110a(a+b)

B（20問）

① −3x²−4xy
= −x(3x+4y)

② −8x²−10xy
= −2x(4x+5y)

③ −15x²−18xy
= −3x(5x+6y)

④ −24x²−28xy
= −4x(6x+7y)

⑤ −35x²−40xy
= −5x(7x+8y)

⑥ −48x²−54xy
= −6x(8x+9y)

⑦ −63x²−70xy
= −7x(9x+10y)

⑧ −80x²−88xy
= −8x(10x+11y)

⑨ −99x²−108xy
= −9x(11x+12y)

⑩ −120x²−130xy
= −10x(12x+13y)

⑪ −3a²−3ab
= −3a(a+b)

⑫ −8a²−8ab
= −8a(a+b)

⑬ −15a²−15ab
= −15a(a+b)

⑭ −24a²−24ab
= −24a(a+b)

⑮ −35a²−35ab
= −35a(a+b)

⑯ −48a²−48ab
= −48a(a+b)

⑰ −63a²−63ab
= −63a(a+b)

⑱ −80a²−80ab
= −80a(a+b)

⑲ −99a²−99ab
= −99a(a+b)

⑳ −120a²−120ab
= −120a(a+b)

C（20問）

① 4x²−5xy
= x(4x−5y)

② 10x²−12xy
= 2x(5x−6y)

③ 18x²−21xy
= 3x(6x−7y)

④ 28x²−32xy
= 4x(7x−8y)

⑤ 40x²−45xy
= 5x(8x−9y)

⑥ 54x²−60xy
= 6x(9x−10y)

⑦ 70x²−77xy
= 7x(10x−11y)

⑧ 88x²−96xy
= 8x(11x−12y)

⑨ 108x²−117xy
= 9x(12x−13y)

⑩ 130x²−140xy
= 10x(13x−14y)

⑪ 4a²−4ab
= 4a(a−b)

⑫ 10a²−10ab
= 10a(a−b)

⑬ 18a²−18ab
= 18a(a−b)

⑭ 28a²−28ab
= 28a(a−b)

⑮ 40a²−40ab
= 40a(a−b)

⑯ 54a²−54ab
= 54a(a−b)

⑰ 70a²−70ab
= 70a(a−b)

⑱ 88a²−88ab
= 88a(a−b)

⑲ 108a²−108ab
= 108a(a−b)

⑳ 130a²−130ab
= 130a(a−b)

D（20問）

① x²−3xy
= x(x−3y)

② 6x²−10xy
= 2x(3x−5y)

③ 15x²−21xy
= 3x(5x−7y)

④ 28x²−36xy
= 4x(7x−9y)

⑤ 45x²−55xy
= 5x(9x−11y)

⑥ 66x²−78xy
= 6x(11x−13y)

⑦ 91x²−105xy
= 7x(13x−15y)

⑧ 120x²−8xy
= 8x(15x−y)

⑨ 9x²−27xy
= 9x(x−3y)

⑩ 30x²−50xy
= 10x(3x−5y)

⑪ 2a²−4ab
= 2a(a−2b)

⑫ 8a²−12ab
= 4a(2a−3b)

⑬ 18a²−24ab
= 6a(3a−4b)

⑭ 32a²−40ab
= 8a(4a−5b)

⑮ 50a²−60ab
= 10a(5a−6b)

⑯ 72a²−84ab
= 12a(6a−7b)

⑰ 98a²−14ab
= 14a(7a−b)

⑱ 16a²−32ab
= 16a(a−2b)

⑲ 36a²−54ab
= 18a(2a−3b)

⑳ 60a²−80ab
= 20a(3a−4b)