Bài 1:
`d,`
`(x^2+2)^3=(x^2)^3+3.(x^{2})^{2}.2+3.x^{2}.2^{2}+2^{3}=x^6+3.x^{4}.2+3.x^{2}.4+8=x^6+6x^4+12x^{2}+8`
`e,`
`(2x+3y)^3=(2x)^3+3.(2x)^{2}.3y+3.2x.(3y)^{2}+(3y)^3=8x^3+3.4x^{2}.3y+3.2x.9y^2+27y^3=8x^3+36x^2y+54xy^2+27y^3`
`f,`
`({1}/{2}x+y^{2})^{3}=({1}/{2}x)^3+3.({1}/{2}x)^{2}.y^2+3.{1}/{2}x.(y^2)^2+(y^2)^3={1}/{8}x^3+3.{1}/{4}x^{2}.y^2+3.{1}/{2}x.y^4+y^6={1}/{8}x^3+{3}/{4}x^{2}y^2+{3}/{2}xy^4+y^6`
Bài 2:
`d,`
`(x^2-2)^3=(x^2)^3-3.(x^{2})^{2}.2+3.x^{2}.2^{2}-2^{3}=x^6-3.x^{4}.2+3.x^{2}.4-8=x^6-6x^4+12x^{2}-8`
`e,`
`(2x-3y)^3=(2x)^3-3.(2x)^{2}.3y+3.2x.(3y)^{2}-(3y)^3=8x^3-3.4x^{2}.3y+3.2x.9y^2-27y^3=8x^3-36x^2y+54xy^2-27y^3`
`f,`
`({1}/{2}x-y^{2})^{3}=({1}/{2}x)^3-3.({1}/{2}x)^{2}.y^2+3.{1}/{2}x.(y^2)^2-(y^2)^3={1}/{8}x^3-3.{1}/{4}x^{2}.y^2+3.{1}/{2}x.y^4-y^6={1}/{8}x^3-{3}/{4}x^{2}y^2+{3}/{2}xy^4-y^6`
Bài 3:
`a,`
`A=(x-1)^3-(x+1)^3=x^3-3x^2+3x-1-(x^3+3x^2+3x+1)=x^3-3x^2+3x-1-x^3-3x^2-3x-1=-6x^2-2`
`b,`
`B=(x+y)^3-(x-y)^3=x^3+3x^2y+3xy^2+y^3-(x^3-3x^2y+3xy^2-y^3)=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3=6x^2y+2y^3`
`c,`
`C=(x-y)^3+3xy(x-y)=x^3-3x^2y+3xy^2-y^3+3x^2y-3xy^2=x^3-y^3`
`d,`
`D=(x+1)^3+(x-3)^3-2(x^2+15)(x-3)=x^3+3x^2+3x+1+x^3-9x^2+27x-27-2(x^3-3x^2+15x-45)=2x^3-6x^2+30x-26-2x^3+6x^2-30x+90=64`
Bài 4:
`a,` `A=x^3+6x^2+12x+8=x^3+3.x^{2}.2+3.x.2^{2}+2^{3}=(x+2)^3`
Thay `x=8` vào `A` có:
`A=(8+2)^3=10^3=1000`
`b,` `B=x^3-3x^2+3x-1=x^3-3.x^{2}.1+3.x.1^{2}-1^{3}=(x-1)^3`
Thay `x=101` vào `B` có:
`B=(101-1)^3=100^3=1000000`
