Đáp án:
Giải thích các bước giải:
9/
a/ $x^3+12x^2+48x+64=(x+4)^3=(6+4)^3=10^3=1000$
b/ $x^3-6x^2+12x-8=(x-2)^3=(22-2)^3=20^3=8000$
c/ $x^3+9x^2+27x+27=(x+3)^3=(-103+3)^3=(-100)^3=-1000000$
d/ $x^3-15x^3+75x-125=(x-5)^3=(25-5)^3=20^3=8000$
10/
a/ $(x-3)(x^2+3x+9)+x(x+2)(2-x)=1$
⇔ $x^3-27-x(x^2-4)-1=0$
⇔ $x^3-28-x^3+4x=0$
⇔ $4x-28=0$
⇔ $x=\frac{28}{4}=7$
b/ $(x+1)^3-(x-1)^3-6(x-1)^2=-10$
⇔ $x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2+12x-6+10=0$
⇔ $12x+6=0$
⇔ $2x+1=0$
⇔ $x=-\frac{1}{2}$
11/
a/ $A=(x-2)^3-x(x-1)(x+1)+6x(x-3)$
$=x^3-6x^2+12x-8-x(x^2-1)+6x^2-18x$
$=x^3-6x-8-x^3+x$
$=-5x-8$
b/ $B=(x-2)(x^2-2x+4)(x+2)(x^2+2x+4)$
$=(x-2)(x^2+2x+4)(x+2)(x^2-2x+4)$
$=(x^3-8)(x^3+8)$
$=x^6-64$
c/ $C=(2x+y)(4x^2-2xy+y^2)-(2x-y)(4x^2+2xy+y^2)$
$=(8x^3+y^3)-(8x^3-y^3)$
$=2y^3$
d/ $D=(x+y)^3-(x-y)^3-2y^3$
$=x^3+3x^2y+3xy^2+y^3-(x^3-3x^2y+3xy^2-y^3)-2y^3$
$=x^3+3x^2y+3xy^2+y^3-x^3+3x^2y-3xy^2+y^3-2y^3$
$=6x^2y$
chúc bạn học tốt !!!
