Đáp án+Giải thích các bước giải:
`a)` `(x-2)(x+2)+(3x-4)(x^2-3x+1)-(3x-2)^2`
`=(x^2-2^2)+(3x^3-13x^2+15x-4)-[(3x)^2-2.3x.2+2^2]`
`=(x^2-2^2)+(3x^3-13x^2+15x-4)-(9x^2-12x+4)`
`=x^2-4+3x^3-13x^2+15x-4-9x^2+12x-4`
`=3x^3+(x^2-13x^2-9x^2)+(15x+12x)-(4+4+4)`
`=3x^3-21x^2+27x-12`
`b)` `(x+2)^3-(x-3)(x^2+3x+9)-(x-2)(6x+1)`
`=(x^3+3.x^2.2+3.x.2^2+2^3)-(x^3-3^3)-(6x^2+x-12x-2)`
`=(x^3+6x^2+12x+8)-(x^3-27)-(6x^2-11x-2)`
`=x^3+6x^2+12x+8-x^3+27-6x^2+11x+2`
`=(x^3-x^3)+(6x^2-6x^2)+(12x+11x)+(8+27+2)`
`=23x+37`
`c)` `(x-4)^2+(1+2x)^3+(x+2)^2-(1-x)(1+x+x^2)`
`=(x^2-2.x.4+4^2)+[1^3+3.1^{2}.2x+2.1.(2x)^2+(2x)^3]+(x^2+2.x.2+2^2)-(1^3-x^3)`
`=x^2-8x+16+1+6x+12x^2+8x^3+x^2+4x+4-1+x^3`
`=(8x^3+x^3)+(12x^2+x^2+x^2)+(6x-8x)+(16+4+1-1)`
`=9x^3+14x^2+2x+20`
`d)` `(x+5)^2-(x+2)(x^2-2x+4)+(x-3)^3-(2x+1)(2x-1)`
`=(x^2+10x+25)-(x^3+2^3)+(x^3-3.x^{2}.3+3.x.3^2-3^3)-[(2x)^2-1^2]`
`=x^2+10x+25-(x^3+8)+(x^3-9x^2+27x-27)-(4x^2-1)`
`=x^2+10x+25-x^3-8+x^3-9x^2+27x-27-4x^2+1`
`=(x^3-x^3)+(x^2-9x^2-4x^2)+(10x+27x)+(25-8-27+1)`
`=-12x^2+37x-9`
