Đáp án:
`a)x^4+2x^3-x^2-2x`
`b)-6x³+17x²+5x-6`
`c)x³+6x²+4x-15`
`d)x³+1`
`e)10x^4+4x^3-15x²-11x-2`
`f)x³-6x²+11x-12`
Giải thích các bước giải:
`a)(x²-1)(x²+2x)`
`=x².x²+x².2x-1.x²-1.2x`
`=x^4+2x^3-x^2-2x`
`b)(2x-1)(3x+2)(3-x)`
`=(2x.3x+2x.2-1.3x-1.2)(3-x)`
`=(6x²+4x-3x-2)(3-x)`
`=6x².3+6x².(-x)+4x.3+4x.(-x)-3x.3-3x.(-x)-2.3-2.(-x)`
`=18x²-6x³+12x-4x²-9x+3x²-6+2x`
`=-6x³+(18x²-4x²+3x²)+(12x-9x+2x)-6`
`=-6x³+17x²+5x-6`
`c)(x+3)(x²+3x-5)`
`=x.x²+x.3x+x.(-5)+3.x²+3.3x+3.(-5)`
`=x³+3x²-5x+3x²+9x-15`
`=x³+(3x²+3x²)+(-5x+9x)-15`
`=x³+6x²+4x-15`
`d)(x+1)(x²-x+1)`
`=x.x²+x.(-x)+x.1+1.x²+1.(-x)+1.1`
`=x³-x²+x+x²-x+1`
`=x³+(-x²+x²)+(x-x)+1`
`=x³+1`
`e)(2x³-3x-1)(5x+2)`
`=2x³.5x+2x³.2-3x.5x-3x.2-1.5x-1.2`
`=10x^4+4x³-15x²-6x-5x-2`
`=10x^4+4x^3-15x²-11x-2`
`f)(x²-2x+3)(x-4)`
`=x².x+x².(-4)-2x.x-2x.(-4)+3.x+3.(-4)`
`=x³-4x²-2x²+8x+3x-12`
`=x³-(4x²+2x²)+(8x+3x)-12`
`=x³-6x²+11x-12`