\(1.2,\\ a,=x^3-3x^2+x^2-3x+x-3=x^3-2x^2-2x-3\\ b,=2x^2-4x^3-6x+12x^2+2-4x=-4x^3+14x^2-10x+2\\ c,=\left(x^2+3x-2\right)\left(3-x\right)\\ =3x^2-x^3+9x-3x^2-6+2x=-x^3+11x-6\)
\(1.3\\ C=5x^2+3x-2-\left(5x^2-14x-3\right)-17x-51\\ C=50\\ D=6x^2+43x-40-\left(6x^2+7x-3\right)-36x+27\\ D=-10\)
\(1.4\\ a,\Leftrightarrow5\left(x^2-10x+21\right)-\left(5x^2-9x-2\right)=25\\ \Leftrightarrow5x^2-50x+105-5x^2+9x+2=25\\ \Leftrightarrow-41x=-82\Leftrightarrow x=2\\ b,\Leftrightarrow3\left(x^2-2x-35\right)-\left(3x^2-x-2\right)=-13\\ \Leftrightarrow3x^2-6x-105-3x^2+x+2=-13\\ \Leftrightarrow-5x=90\Leftrightarrow x=-18\)
\(1.5\\ A=12x-8-15x^2+10x+3x-6-2x^2+4x\\ A=-17x^2+29x-14\\ A=-17\left(-2\right)^2+29\left(-2\right)-14=-68-58-14=-140\)
Bài 1.1
a.
$A=(12x^2+4x-3x-1)-(x-3)(5x+x-4)$
$=(12x^2+x-1)-(x-3)(6x-4)=(12x^2+x-1)-(6x^2-4x-18x+12)$
$=12x^2+x-1-6x^2+22x-12$
$=6x^2+23x-13$
b.
$B=(5x^2+3x-2)-(3x^3-3x^2-9x)-2x(x^2-9x+20)$
$=(5x^2+3x-2)-(3x^3-3x^2-9x)-(2x^3-18x^2+40x)$
$=5x^2+3x-2-3x^3+3x^2+9x-2x^3+18x^2-40x$
$=-5x^3+26x^2-28x-2$
Bài 1.2:
a.
$(x^2+x+1)(x-3)=x(x^2+x+1)-3(x^2+x+1)$
$=x^3+x^2+x-3x^2-3x-3=x^3-2x^2-2x-3$
b.
$B=2(x^2-3x+1)-4x(x^2-3x+1)$
$=2x^2-6x+2-(4x^3-12x^2+4x)=2x^2-6x+2-4x^3+12x^2-4x$
$=-4x^3+14x^2-10x+2$
c.
$C=(x^2+3x-2)(3+x-2x)=(x^2+3x-2)(3-x)$
$=3(x^2+3x-2)-x(x^2+3x-2)$
$=3x^2+9x-6-(x^3+3x^2-2x)$
$=3x^2+9x-6-x^3-3x^2+2x$
$=-x^3+11x-6$
Bài 1.3
a.
$C=(5x^2+5x-2x-2)-(5x^2+x-15x-3)-(17x+51)$
$=5x^2+3x-2-5x^2+14x+3-17x-51$
$=(5x^2-5x^2)+(3x+14x-17x)+(-2+3-51)=-50$ không phụ thuộc vào giá trị của biến
b.
$D=(6x^2+48x-5x-40)-(6x^2+9x-2x-3)-(36x-27)$
$=(6x^2+43x-40)-(6x^2+7x-3)-(36x-27)$
$=6x^2+43x-40-6x^2-7x+3-36x+27$
$=(6x^2-6x^2)+(43x-7x-36x)+(-40+3+27)=-10$ không phụ thuộc vào giá trị của biến
Bài 1.4
a.
PT $\Leftrightarrow 5(x^2-10x+21)-(5x^2-9x-2)=25$
$\Leftrightarrow 5x^2-50x+105-5x^2+9x+2=25$
$\Leftrightarrow -41x+82=0$
$\Leftrightarrow 41x=82\Leftrightarrow x=2$
b.
PT $\Leftrightarrow 3(x^2-2x-35)-(3x^2-x-2)=-13$
$\Leftrightarrow 3x^2-6x-105-3x^2+x+2=-13$
$\Leftrightarrow -5x-90=0$
$\Leftrightarrow x=-18$
Bài 1.5
a.
$A=(12x-8-15x^2+10x)+(3x-6-2x^2+4x)$
$=-15x^2+22x-8+7x-2x^2-6$
$=-17x^2+29x-14=-17.(-2)^2+29(-2)-14=-140$
