Rút gọn biểu thức sau

Đáp án + Giải thích các bước giải:

$3)$ `(x+2y)^2 - (x-2y )^2`

`= [ (x+2y) + (x-2y)][(x+2y)-(x-2y)]`

`= [ ( x + x ) + ( 2y - 2y )][ ( x - x ) + ( 2y + 2y )]`

`= ( 2x ) * ( 4y )`

`= 8xy`

`-----`

$6)$ `(3x-2)^2 - ( 3x -1 )^2`

`= [ ( 3x - 2 ) + ( 3x - 1 )][ ( 3x - 2 ) - ( 3x - 1 ) ]`

`= [ ( 3x + 3x ) - ( 2 + 1 )][ ( 3x - 3x ) - ( 2 - 1 )]`

`= (6x - 3) * ( -1 )`

`= -6x + 3`

`-----`

$9)$ `( -2x + 3 )^2 - ( 5x - 3 )^2`

`= [ ( -2x + 3 ) + ( 5x -3  )][ ( -2x + 3 ) - ( 5x - 3 )]`

`= [ ( -2x + 5x ) + ( 3 - 3 )][(-2x - 5x ) + ( 3 + 3 )]`

`= ( -3x ) * ( -7x + 6 )`

`= 21x^2 - 18x`

`-----`

$12)$ `-(x+1)^2 + ( x - 1 )^2`

`= (x-1)^2 - (x+1)^2`

`= [(x-1)+(x+1)][(x-1)-(x+1)]`

`= [(x+x)+(1-1)][(x-x)-(1+1)]`

`= ( 2x ) * (-2)`

`= -4x`

`-----`

$15)$ `-(2x+7)^2 + (-2x-3)^2`

`= (-2x-3)^2 - (2x+7)^2`

`= [(-2x-3)+(2x+7)][(-2x-3)-(2x+7)]`

`= [(-2x+2x)+(7-3)][(-2x-2x)-(3+7)]`

`= 4 * ( -4x - 10 )`

`= -16x - 40`