Đáp án:
`a)-28`
`b)10`
`c)3x+125`
`d)1`
Giải thích các bước giải:
`a)(2x-3)(4x²+6x+9)-(2x+1)(4x²-2x+1)`
`=(2x-3)[(2x)²+2x.3+3²]-(2x+1)[(2x)²-2x.1+1²]`
`=(2x)³-3³-[(2x)³+1³]`
`=8x³-27-(8x³+1)`
`=8x³-27-8x³-1`
`=(8x³-8x³)-(27+1)`
`=-28`
`b)(x+2)(x²-2x+4)-(x³-2)`
`=(x+2)(x²-x.2+2²)-(x³-2)`
`=x³+2³-x³+2`
`=x³+8-x³+2`
`=(x³-x³)+(8+2)`
`=10`
`c)(3x+5)(9x²-15x+25)-3x(3x-1)(3x+1)`
`=(3x+5)[(3x)²-3x.5+5²]-3x[(3x)²-1²]`
`=(3x)³+5³-3x(9x²-1)`
`=27x³+125-27x³+3x`
`=(27x³-27x³)+3x+125`
`=3x+125`
`d)x^6-(x²+x+1)(x²-1)(x²-x+1)`
`=x^6-(x²+x+1)(x+1)(x-1)(x²-x+1)`
`=x^6-[(x+1)(x²-x+1)][(x-1)(x²+x+1)]`
`=x^6-(x³+1)(x³-1)`
`=x^6-[(x^3)^2-1^2]`
`=x^6-(x^6-1)`
`=x^6-x^6+1`
`=(x^6-x^6)+1`
`=1`
