Đáp án:
`a)4xy`
`b)x^6-1/27`
`c)x^6-64`
`d)2y³`
`e)x²`
Giải thích các bước giải:
`a)(x+y)²-(x-y)²`
`=(x+y+x-y)(x+y-x+y)`
`=2x.2y`
`=4xy`
`b)(x²-1/3)(x^4+1/3x²+1/9)`
`=(x²-1/3)[(x^2)^2+x². 1/3+(1/3)^2]`
`=(x^2)^3-(1/3)^3`
`=x^6-1/27`
`c)(x-2)(x²-2x+4)(x+2)(x²+2x+4)`
`=[(x-2)(x²+2x+4)][(x+2)(x²-2x+4)]`
`=[(x-2)(x²+x.2+2²)][(x+2)(x²-x.2+2²)]`
`=(x³-2³)(x³+2³)`
`=(x³-8)(x³+8)`
`=(x^3)^2-8^2`
`=x^6-64`
`d)(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`
`e)(2x-3)²-(2x-3)(2x-6)+(x-3)²`
`=(2x-3)²-2.(2x-3).(x-3)+(x-3)²`
`=[(2x-3)-(x-3)]²`
`=(2x-3-x+3)²`
`=x²`
