Đáp án+Giải thích các bước giải:
Bài 1:
`a) (2x+1/3y)^3`
`=(2x)^3+3.(2x)^2 . 1/3y+3.2x . (1/3y)^2 +(1/3y)^3`
`=8x^3+ 4x^2y+2/3xy^2+1/(27)y^3`
`b)(3x+1/4y)^3`
`=(3x)^3+3.(3x)^2 . 1/4y+3.3x . (1/4y)^2 +(1/4y)^3`
`=27x^3+ (27)/4x^2y+9/(16)xy^2+1/(64)y^3`
`c) 8x^3-1/(27)y^3`
`=(2x)^3-(1/3y)^3`
`=(2x-1/3y)[(2x)^2+2x. 1/3y+(1/3y)^2]`
`=(2x-1/3y)(4x^2+2/3xy+1/9y^2)`
`d) x^3+8y^3`
`=x^3+(2y)^3`
`=(x+2y)[x^2-x.2y+(2y)^2]`
`=(x+2y)(x^2-2xy+4y^2)`
Bài 2:
`a) x^3+6x^2y+12xy^2+8y^3`
`=x^3+3.x^2 . 2y+3.x.(2y)^2+(2y)^3`
`=(x+2y)^3`
`b) 125-225y+125y^2-27y^3 -> ` Sửa: ` 125-225y+135y^2-27y^3`
` 125-225y+135y^2-27y^3`
`=5^3-3.5^2 . 3y+3.5.(3y)^2-(3y)^3`
`= (5-3y)^3`
`c) x^3-6x^2+12x-8`
`=x^3-3.x^2 .2+3.x.2^2-2^3`
`=(x-2)^3`
Bài 3:
`a) (3x+y)(9x^2-3xy+y^2)`
`=(3x+y)[(3x)^2-3x.y+y^2]`
`=(3x)^3+y^3`
`=27x^3+y^3`
`b) (1/2x+4y)(1/4x^2-2xy+16y^2)`
`=(1/2x+4y)[(1/2x)^2-1/2x . 4y +(4y)^2]`
`=(1/2x)^3+(4y)^3`
`= 1/8x^3+64y^3`
`c) (2x+7y)(4x^2-14xy+49y^2)`
`=(2x+7y)[(2x)^2-2x.7y+(7y)^2]`
`=(2x)^3+(7y)^3`
`=8x^3+343y^3`
Bài 4:
`a) (2x-y)(4x^2+2xy+y^2)`
`=(2x-y)[(2x)^2+2x.y+y^2]`
`=(2x)^3-y^3`
`=8x^3-y^3`
`b) (x-3y)(x^2+3y+9y^2)->` Sửa ` (x-3y)(x^2+3xy+9y^2)`
` (x-3y)(x^2+3xy+9y^2)`
`=(x-3y)[x^2+x.3y+(3y)^2]`
`=x^3-(3y)^3`
`=x^3-27y^3`
