Đáp án + Giải thích các bước giải:
Câu `3` :
`a)` `A=(2x-1/2)^2-(x-3)(4x-1)`
`=4x^2-2*2x*1/2+(1/2)^2-(4x^2-x-12x+3)`
`=4x^2-2x+1/4-4x^2+x+12x-3`
`=11x-11/4`
`b)` `B=(3x-1)(3x+1)-(2+3x)^2`
`=9x^2-1-(4+12x+9x^2)`
`=9x^2-1-4-12x-9x^2`
`=-5-12x`
`c)` `(x^2-2)(x+3)-(x-1/3)^3`
`=x^3+3x^2-2x-6-[x^3-3*x^2*1/3+3*x*(1/3)^2-(1/3)^3]`
`=x^3+3x^2-2x-6-(x^3-x^2+1/3x-1/27)`
`=x^3+3x^2-2x-6-x^3+x^2-1/3x+1/27`
`=4x^2-7/3x-161/27`
`d)` `D=(3x-1)^2-(3x-2)^2`
`=[(3x-1)-(3x-2)][(3x-1)+(3x-2)]`
`=(3x-1-3x+2)(3x-1+3x-2)`
`=1(6x-3)=6x-3`
`e)` `E=9x^3-(2x-1)(4x^2+2x+1)`
`=9x^3-(2x-1)[(2x)^2+2x*1+1^2]`
`=9x^3-[(2x)^3-1]`
`=9x^3-(8x^3-1)`
`=9x^3-8x^3+1=x^3+1`
`=(x+1)(x^2-x+1)`
`f)` `F=(3x+2)(9x^2-6x+4)-27x^3`
`=(3x+2)[(3x)^2-3x*2+2^2]-27x^3`
`=(3x)^3+2^3-27x^3`
`=27x^3+8-27x^3=8`
`g)` `(2x^2-3x+1)^2+(3x-1)^2-2(2x^2-3x+1)(1-3x)`
`=(2x^2-3x+1)^2-2(2x^2-3x+1)(1-3x)+(3x-1)^2`
`=(2x^2-3x+1)^2+2(2x^2-3x+1)(3x-1)+(3x-1)^2`
`=(2x^2-3x+1+3x-1)^2`
`=(2x^2)^2=4x^4` .
