Bài 1:
`a)-2x³.(x²+5x-1)`
`=-2x³.x²-2x³.5x-2x³.(-1)`
`=-2x^5-10x^4+2x³`
`b)2x.(x²-3)`
`=2x.x²-2x.3`
`=2x³-6x`
`c)(2x+3y)(2x-3y)`
`=(2x)²-(3y)²`
`=4x²-9y²`
`d)(5x-2y)(x²-xy+1)`
`=5x(x²-xy+1)-2y(x²-xy+1)`
`=5x³-5x²y+5x-2x²y+2xy²-2y`
`=5x³-(5x²y+2x²y)+2xy²+5x-2y`
`=5x³-7x²y+2xy²+5x-2y`
`e)(x+1)(x-1)(x+2)`
`=(x²-1)(x+2)`
`=x²(x+2)-1(x+2)`
`=x³+2x²-x-2`
Bài 2:
`A=(x-1)(x+5)-x(x+4)`
`=x²+5x-x-5-x²-4x`
`=(x²-x²)+(5x-x-4x)-5`
`=-5`
`B=3x(x²-4x³+5)-(3x²+15x-7)`
`=3x³-12x^4+15x-3x²-15x+7`
`=-12x^4+3x³-3x²+(15x-15x)+7`
`=-12x^4+3x³-3x²+7`
Bài 3:
`(x-1)(4x-3)-4x(x-5)=5`
`⇔4x²-3x-4x+3-4x²+20x=5`
`⇔(4x²-4x²)+(-3x-4x+20x)+3=5`
`⇔13x+3=5`
`⇔13x=5-3`
`⇔13x=2`
`⇔x=2/13`
Vậy `x=2/13`
Bài 4:
`A=(2x+3)(4x²-6x+9)-2(4x³-1)-2x`
`=(2x+3)[(2x)²-2x.3+3²]-8x³+2-2x`
`=(2x)³+3³-8x³+2-2x`
`=8x³+27-8x³+2-2x`
`=(8x³-8x³)-2x+(27+2)`
`=-2x+29`
Thay `x=2021` vào biểu thức `A` ta được:
`A=-2.2021+29=-4042+29=-4013`
Vậy giá trị của biểu thức `A` tại `x=2021` là `-4013`