Đáp án+Giải thích các bước giải:

 Bài `18:`

`a)(2x^{2}+1/3)^{3}`

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

`=8x^{6}+4x^{4} +2/3x^{2}+1/27`

`b)(2x^{2}y-3xy)^{3}`

`=(2x^{2}y)^{3}-3.(2x^{2}y)^{2}.3xy+3.2x^{2}y.(3xy)^{2}-(3xy)^{3}`

`=8x^{6}y^{3}-36x^{5}y^{3}+54x^{4}y^{3}-27x^{3}y^{3}`

`c)(-3xy^{4}+1/2x^{2}y^{2})^{3}=[-(3xy^{4}-1/2x^{2}y^{2})]^{3}`

`=(3xy^{4}-1/2x^{2}y^{2])^{3}`

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

`=27x^{3}y^{12}-\frac{27}{2}x^{4}y^{10}+9/4x^{5}y^{8}-1/8x^{6}y^{6}`

`d)(-1/3ab^{2}-2a^{3}b)^{3}=[-(1/3ab^{2}+2a^{3}b)]^{3}`

`=-(1/3ab^{2}+2a^{3}b)^{3}`

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

`=-[1/27a^{3}b^{6}+ 2/3a^{5}b^{5}+4a^{7}b^{4}+8a^{9}b^{3}]`

`=-1/27 a^{3}b^{6}-2/3a^{5}b^{5}-4a^{7}b^{4}-8a^{9}b^{3}`

`e)(x+1)^{3}-(x-1)^{3}-6.(x-1).(x+1)`

`=(x+1-x+1).[(x+1)^{2}+(x+1).(x-1)+(x-1)^{2}]-6.(x^{2}-1^{2})`

`=2.(x^{2}+2.x.1+1^{2}+x^{2}-1^{2}+x^{2}-2.x.1+1^{2})-6x^{2}+6`

`=2.(3x^{2}+1)-6x^{2}+6`

`=6x^{2}+2-6x^{2}+6`

`=8`

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

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

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

`=(x-1).(-1)`

`=1-x`

`g)(x-1)^{3}-(x+2).(x^{2}-2x+4)+3.(x+4).(x-4)`

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

`=x^{3}-3x^{2}+3x-1-(x^{3}+2^{3})+3x^{2}-48`

`=x^{3}+(3x^{2}-3x^{2})+3x-49-x^{3}-8`

`=(x^{3}-x^{3})+3x-(49+8)`

`=3x-57`

`h)3x^{2}.(x+1).(x-1)+(x^{2}-1)^{3}-(x^{2}-1).(x^{4}+x^{2}+1)`

`=3x^{2}.(x^{2}-1^{2})+(x^{2}-1).[(x^{2}-1)^{2}-(x^{4}+x^{2}+1)]`

`=3x^{2}.(x^{2}-1)+(x^{2}-1).[(x^{2})^{2}-2.x^{2}.1+1^{2}-x^{4}-x^{2}-1]`

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

`=(x^{2}-1).[(3x^{2}-2x^{2}-x^{2})+(x^{4}-x^{4})+(1-1)]`

`=(x^{2}-1).0`

`=0`

`k)(x^{4}-3x^{2}+9).(x^{2}+3)+(3-x^{2})^{3}-9x^{2}.(x^{2}-3)`

`=(x^{2}+3).[(x^{2})^{2}-x^{2}.3+3^{2}]+[-(x^{2}-3)]^{3}-9x^{2}.(x^{2}-3)`

`=[(x^{2})^{3}+3^{3}]-(x^{2}-3)^{3}-9x^{2}.(x^{2}-3)`

`=(x^{6}+27)-(x^{2}-3).[(x^{2}-3)^{2}+9x^{2}]`

`=x^{6}+27-(x^{2}-3).[(x^{2})^{2}-2.x^{2}.3+3^{2}+9x^{2}]`

`=x^{6}+27-(x^{2}-3).[(x^{2})^{2}+x^{2}.3+3^{2}]`

`=x^{6}+27-[(x^{2})^{3}-3^{3}]`

`=x^{6}+27-x^{6}+27`

`=54`

`l)(4x+6y).(4x^{2}-6xy+9y^{2})-54y^{3}`

`=2.(2x+3y).[(2x)^{2}-2x.3y+(3y)^{2}]-54y^{3}`

`=2.[(2x)^{3}+(3y)^{3}]-54y^{3}`

`=2.(8x^{3}+27y^{3})-54y^{3}`

`=16x^{3}+54y^{3}-54y^{3}`

`=16x^{3}`

Bài `19:`

`a)x^{3}+8=x^{3}+2^{3}=(x+2).(x^{2}-x.2+2^{2})`

`=(x+2).(x^{2}-2x+4)`

`b)27-8y^{3}=3^{3}-(2y)^{3}=(3-2y).[3^{2}+3.2y+(2y)^{2}]`

`=(3-2y).(9+6y+4y^{2})`

`c)y^{6}+1=(y^{2})^{3}+1^{3}=(y^{2}+1).[(y^{2})^{2}-y^{2}.1+1^{2}]`

`=(y^{2}+1).(y^{4}-y^{2}+1)`

`d)64x^{3}-1/8y^{3}=(4x)^{3}-(1/2y)^{3}`

`=(4x-1/2y).[(4x)^{2}+4x . 1/2y+(1/2y)^{2}]`

`=(4x-1/2y).(16x^{2}+2xy+1/4y^{2})`

`e)125x^{6}-27y^{9}=(5x^{2})^{3}-(3y^{3})^{3}`

`=(5x^{2}-3y^{3}).[(5x^{2})^{2}+5x^{2}. 3y^{3}+(3y^{3})^{2}]`

`=(5x^{2}-3y^{3}).(25x^{4}+15x^{2}y^{3}+9y^{6})`

`f)-\frac{x^{6}}{125}-\frac{y^{3}}{64}`

`=-[(\frac{x^{2}}{5})^{3}+(y/4)^{3}]`

`=-(\frac{x^{2}}{5}+y/4).[(\frac{x^{2}}{5})^{2}-\frac{x^{2}}{5}. y/4+(y/4)^{2}]`

`=-(\frac{x^{2}}{5}+y/4).(\frac{x^{4}}{25}-\frac{x^{2}y}{20}+\frac{y^{2}}{16})`

`g)16x^{2}.(4x-y)-8y^{2}.(x+y)+xy.(16x+8y)`

`=64x^{3}-16x^{2}y-8xy^{2}-8y^{3}+16x^{2}y+8xy^{2}`

`=64x^{3}+(16x^{2}y-16x^{2}y)+(8xy^{2}-8xy^{2})-8y^{3}`

`=(4x)^{3}-(2y)^{3}`

`=(4x-2y).[(4x)^{2}+4x.2y+(2y)^{2}]`

`=(4x-2y).(16x^{2}+8xy+4y^{2})`

`=2.(2x-y).4.(4x^{2}+2xy+y^{2})`

`=8.(2x-y).(4x^{2}+2xy+y^{2})`