Đáp án:

 

Giải thích các bước giải:

a/ $x^3-3x^2+1-3x$

$=x^3+x^2-4x^2-4x+x+1$

$=x^2(x+1)-4x(x+1)+(x+1)$

$=(x+1)(x^2-4x+1)$

$=(x+1)(x^2-4x+4-3)$

$=(x+1)[(x-2)^2-3]$

$=(x+1)(x-2-\sqrt{3})(x-2+\sqrt{3})$

b/ $(a^2+1)^2-4a^2$

$=(a^2+1)^2-(2a)^2$

$=(a^2+1-2a)(a^2+1+2a)$

c/ $x^3-3x^2-4x+12$

$=x^2(x-3)-4(x-3)$

$=(x-3)(x^2-4)$

$=(x-3)(x-2)(x+2)$

d/ $x(x+y)-5x-5y$

$=x(x+y)-5(x+y)$

$=(x+y)(x-5)$

e/ $x^2-y^2-2xy+y^2$

$=(x^2-2xy+y^2)-y^2$

$=(x-y)^2-y^2$

$=(x-y-y)(x-y+y)$

$=x(x-2y)$

f/ $x^2-y^2+4-4x$

$=(x^2-4x+4)-y^2$

$=(x-2)^2-y^2$

$=(x-2-y)(x-2+y)$

$=(x-y-2)(x+y-2)$

Chúc bạn học tốt !!!

TL:

$a) x^3 - 3x^2 + 1 - 3x = x^2 ( 1 - 3x ) + ( 1 - 3 ) = ( 1 - 3x ) ( x^2 + 1 )$

$b) ( x^2 - 1^2 )^2 - 4a^2 = ( a^2 + 1 )^2 - 4a^2 = ( 1-a^2) ( 3a^2 + 1 )$

$c) x^3 - 3x^2 - 4x + 12 = x^2 ( x - 3 ) - 4 ( x - 3 ) = ( x - 2 )( x + 2 )(x - 3 )$

$d) x( x + y ) - 5x - 5y = x (x + y ) - 5 (x + y) = (x + y)(x - 5)$

$e) x^2 - y^2 -2xy + y^2 = x^2 - 2xy + y^2 - y^2$

$= ( x - y )^2 - y^2 = ( x - y - y ) ( x - y + y ) = x(x-2y)$

$ f)  x^2 - y^2 + 4 - 4x = ( x^2 - 4x + 4 ) - y^2 = ( x - y -2 ) ( x + y - 2 ) $