Đáp án:
`a)-27`
`b)2y³`
`c)8x²+4x+4`
Giải thích các bước giải:
`a)(x+3)(x²-3x+9)-(54+x³)`
`=(x+3)(x²-x.3+3²)-54-x³`
`=x³+3³-54-x³`
`=x³+27-54-x³`
`=(x³-x³)+(27-54)`
`=-27`
`b)(2x+y)(4x²-2xy+y²)-(2x-y)(4x²+2xy+y²)`
`=(2x+y)[(2x)²-2x.y+y²]-(2x-y)[(2x)²+2x.y+y²]`
`=(2x)³+y³-[(2x)³-y³]`
`=8x³+y³-(8x³-y³)`
`=8x³+y³-8x³+y³`
`=(8x³-8x³)+(y³+y³)`
`=2y³`
`c)(x+2)³-(x-2)(x²+8)-20`
`=x³+3.x².2+3.x.2²+2³-(x³+8x-2x²-16)-20`
`=x³+6x²+12x+8-x³-8x+2x²+16-20`
`=(x³-x³)+(6x²+2x²)+(12x-8x)+(8+16-20)`
`=8x²+4x+4`
