Đáp án+Giải thích các bước giải:

 `1)x^{2}-25y^{2}=x^{2}-(5y)^{2}=(x-5y).(x+5y)`

`2)27x^{3}y^{3}-1=(3xy)^{3}-1^{3}`

`=(3xy-1).[(3xy)^{2}+3xy.1+1^{2}]`

`=(3xy-1).(9x^{2}y^{2}+3xy+1)`

`3)8x^{3}+1/27=(2x)^{3}+(1/3)^{3}`

`=(2x+1/3).[(2x)^{2}-2x. 1/3+(1/3)^{2}]`

`=(2x+1/3).(4x^{2}-2/3 x+1/9)`

`4)100x^{4}-1=(10x^{2})^{2}-1^{2}`

`=(10x^{2}-1).(10x^{2}+1)`

`=[(x\sqrt{10})^{2}-1^{2}].(10x^{2}+1)`

`=(x\sqrt{10}-1).(x\sqrt{10}+1).(10x^{2}+1)`

`5)1/27x^{3}+1000y^{6}`

`=(1/3x)^{3}+(10y^{2})^{3}`

`=(1/3x+10y^{2}).[(1/3x)^{2}-1/3x. 10y^{2}+(10y^{2})^{2}]`

`=(1/3x+10y^{2}).(1/9x^{2}-(10)/(3)xy^{2}+100y^{4})`