`1)`
`a)(x²-2x+3)(1/2x-4)`
`=1/2x^3-4x^2-x^2+8x+3/2x-12`
`=1/2x^3-(4x^2+x^2)+(8x+3/2x)-12`
`=1/2x^3-5x^2+19/2x-12`
`b)(x^2-2xy+y^2)(x-y)=(x-y)^2(x-y)=(x-y)^3`
`c)(x-y)(x+y)-(x+2xy+y^2)(-2)`
`=x^2-y^2+2x+4xy+2y^2`
`=x^2+(-y^2+2y^2)+2x+4xy`
`=x^2+y^2+2x+4xy`
`d)(3/2x-1)(3/2x+1)-(3/2x+3)(3/2x-1)`
`=9/4x^2-1-(9/4x^2-3/2x+9/2x-3)`
`=9/4x^2-1-9/4x^2+3/2x-9/2x+3`
`=(9/4x^2-9/4x^2)+(3/2x-9/2x)+(-1+3)`
`=-6/2x+2`
`=-3x+2`
`2)`
`a)(12x-5)(4x-1)+(3x-7)(1-16x)=81`
`⇔48x²-12x-20x+5+3x-48x²-7+112x=81`
`⇔(48x²-48x²)+(-12x-20x+3x+112x)+(5-7)=81`
`⇔83x-2=81`
`⇔83x=81+2`
`⇔83x=83`
`⇔x=83:83`
`⇔x=1`
Vậy `x=1`
`b)(2x+5)(2x-5)-x(4x-3)=-5`
`⇔4x²-25-4x²+3x=-5`
`⇔(4x²-4x²)+3x-25=-5`
`⇔3x-25=-5`
`⇔3x=-5+25`
`⇔3x=20`
`⇔x=20/3`
Vậy `x=20/3`
`c)(x+1)(x²+2x+1)-x²(x+3)=0`
`⇔(x+1)³-x³-3x²=0`
`⇔x³+3x²+3x+1-x³-3x²=0`
`⇔(x³-x³)+(3x²-3x²)+3x+1=0`
`⇔3x+1=0`
`⇔3x=-1`
`⇔x=-1/3`
Vậy `x=-1/3`
