Đáp án:
Giải thích các bước giải:
a/ $x^2(x-1)-x+1$
$=x^2(x-1)-(x-1)$
$=(x-1)(x^2-1)$
$=(x-1)(x-1)(x+1)$
$=(x-1)^2(x+1)$
b/ $(a+b)^3-(a-b)^3$
$=[(a+b)-(a-b)][(a+b)^2+(a+b)(a-b)+(a-b)^2]$
$=2b(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2)$
$=2b(3a^2+b^2)$
c/ $6x(x-3)+9-3x^2$
$=6x^2-18x+9-3x^2$
$=3x^2-18x+9$
$=3(x^2-6x+3)$
$=3(x^2-6x+9-6)$
$=3[(x-3)^2-6]$
$=3(x-3-\sqrt{6})(x-3+\sqrt{6})$
d/ $x(x-y)-5x+5y$
$=x(x-y)-5(x-y)$
$=(x-y)(x-5)$
e/ $3(x+4)-x^2-4x$
$=3(x+4)-x(x+4)$
$=(x+4)(3-x)$
f/ $x^2+4x-y^2+4$
$=(x^2+4x+4)-y^2$
$=(x+2)^2-y^2$
$=(x+2-y)(x+2+y)$
$=(x-y+2)(x+y+2)$
g/ $x^2+5x$
$=x(x+5)$
h/ $-x^2+2x+2y+y^2$
$=-(x^2-2x+1)+(y^2+2y+1)$
$=(y+1)^2-(x-1)^2$
$=(y+1-x+1)(y+1+x-1)$
$=(y-x+2)(x+y)$
Chúc bạn học tốt !!!
