1) Thực hiện các phép tính sau: a) (2x - y)(4x2 - 2xy + y2) b) (2x3 - 21x2 + 67x - 60): (x - 5) 2) Rút gọn các biểu thức sau: a) (x + y)2 - (x - y)2 b) (a + b)3 + (a - b)3 - 2a3

1a) $=8x^3-8x^2y+4xy^2-y^3$

$b) $=\left(2x-3\right)\left(x-4\right)$

`2.` 

$a)

$=4xy$

$b)$

$=6ab^2$

Giải thích các bước giải:

`1)`

`a)(2x-y)(4x^2 -2xy+y^2)`

`=2x(4x^2 -2xy+y^2)-y(4x^2 -2xy+y^2)`

`=8x^3 -4x^2 y+2xy^2 -4x^2 y+2xy^2 -y^3`

`=8x^3 -8x^2 y+4xy^2 -y^3`

`b) (2x^3 -21x^2 +67x-60):(x-5)`

`=(2x^3 -3x^2 -18x^2 +27x+40x-60):(x-5)`

`=[x^2 (2x-3)-9x(2x-3)+20(2x-3)]:(x-5)`

`=(x^2 -9x+20)(2x-3):(x-5)`

`=(x^2 -4x-5x+20)(2x-3):(x-5)`

`=[x(x-4)-5(x-4)](2x-3):(x-5)`

`=(x-5)(x-4)(2x-3):(x-5)`

`=2x^2 -8x-3x+12`

`=2x^2 -11x+12`

`2)`

`a)(x+y)^2 -(x-y)^2`

`=[x+y-(x-y)][x+y+(x-y)]`

`=(x+y-x+y)(x+y+x-y)`

`=2y.2x`

`=4xy`

`b)(a+b)^3 +(a-b)^3 -2a^3`

`=a^3 +3a^2 b+3ab^2 +b^3 +a^3 -3a^2 b+3ab^2 -b^3 -2a^3`

`=6ab^2`