Đáp án + Giải thích các bước giải:
Bài `1` :
`a)` `(3a+1)^3=(3a)^3+3*(3a)^2*1+3*3a*1^2+1^3`
`=27a^3+27a^2+9a+1`
`b)` `(4-2b)^3=4^3-3*4^2*2b+3*4*(2b)^2-(2b)^3`
`=64-96b+48b^2-8b^3`
`c)` `(2c+3d)^3=(2c)^3+3*(2c)^2*3d+3*2c*(3d)^2+(3d)^3`
`=8c^3+36c^2d+54cd^2+27d^3`
`d)` `((3x)/y-(2y)/x)^3=((3x)/y)^3-3*((3x)/y)^2*((2y)/x)+3*(3x)/y*((2y)/x)^2-((2y)/x)^3`
`=(27x^3)/(y^3)-3*(9x^2)/(y^2)*(2y)/x+3*(3x)/y*(4y^2)/x^2-(8y^3)/x^3`
`=(27x^3)/(y^3)-(54x)/y+(36y)/x-(8y^3)/x^3`
Bài `2` :
`a)` `(x+1/2)(x^2-1/2x+1/4)`
`=(x+1/2)[x^2-1/2x+(1/2)^2]`
`=x^3+(1/2)^3=x^3+1/8`
`b)` `(x-3y)(x^2+3xy+9y^2)`
`=(x-3y)[x^2+3xy+(3y)^2]`
`=x^3-(3y)^3=x^3-27y^3`
`c)` `(x^2+3)(x^4-3x^2+9)`
`=(x^2+3)[(x^2)^2-3x^2+3^2]`
`=(x^2)^3+3^3=x^6+27`
`d)` `(2x-1)(4x^2+2x+1)`
`=(2x-1)[(2x)^2+2x*1+1^2]`
`=(2x)^3-1^3=8x^3-1`.
