Đáp án:
Bài 1:
`a,(x^2+2)^3=x^6+6x^4+12x^2+8`
`b,(3x+2y)^3=27x^3+54x^{2}y+36xy^2+8y^3`
Bài 2:
`a,(3x-1)^3=27x^3-27x^2+9x-1`
`b,(x-y/3)^3=x^3-x^2y+{xy^2}/{3}-{y^3}/{27}`
Bài 3:
`a,-8x^3 +12x^2-6x+1=(1-2x)^3`
`b,x^3/64-3/8x^2+3x-8=(x/4-2)^3`
Giải thích các bước giải:
Bài 1:
`a,(x^2+2)^3=(x^2)^3+3.(x^2)^{2}.2+3.x^{2}.2^2+2^3` `=x^6+3x^{4}.2+3.x^{2}.4+8=x^6+6x^4+12x^2+8`
`b,(3x+2y)^3=(3x)^3+3.(3x)^{2}.2y+3.3x.(2y)^{2}+(2y)^3` `=27x^3+3.9x^{2}.2y+3.3x.4y^2+8y^3=27x^3+54x^{2}y+36xy^2+8y^3`
Bài 2:
`a,` `(3x-1)^3=(3x)^3-3.(3x)^{2}.1+3.3x.1^2-1^3`
`=27x^3-3.9x^{2}.1+3.3x.1-1=27x^3-27x^2+9x-1`
`b,` `(x-y/3)^3=x^3-3.x^{2}.y/3+3.x.(y/3)^2-(y/3)^3`
`=x^3-3.x^{2}.y/3+3.x.{y^2}/{9}-{y^3}/{27}=x^3-x^2y+{xy^2}/{3}-{y^3}/{27}`
Bài 3:
`a,` `-8x^3 +12x^2-6x+1=1-6x+12x^2-8x^3`
`=1^3-3.1.2x+3.1.(2x)^{2}-(2x)^3=(1-2x)^3`
`b,` `x^3/64-3/8x^2+3x-8=x^3/64-{3x^2}/8+3x-8`
`=(x/4)^3-3.(x/4)^(2).2+3.{x}/{4}.2^(2)-2^3=(x/4-2)^3`
