Đáp án:
$1)
a)x^4y-5x^2y^2+3x^2y^3\\
b) -6x^2+15x^3-3x^4\\
c) 6x^2+14x-10x^2+6x^3\\
d) 5x-12x^2-6x^3+12x^4\\
e) 5x^3-14x^2+8x\\
f) 3x^3-6x^2y+2xy-4y^2\\
g) x^3-3x^2y+3xy^2-y^3\\
h) 6x^2+2x-3x-1+9x-6x^2+12-8x=11\\
i)12x^2+10x-38\\
k) 18x-34\\
2)
a) x=-2\\
b) x=\dfrac{9}{8}\\$
Giải thích các bước giải:
$1)
a)x^2y(x^2-5y+3y^2)=x^2y.x^2-x^2y.5y+x^2y.3y^2=x^4y-5x^2y^2+3x^2y^3\\
b) -3x^2(2-5x+x^2)=-3x^2.2+3x^2.5x-3x^2.x^2=-6x^2+15x^3-3x^4\\
c) 6x^2+2x(7-5x+3x^2)=6x^2+2x.7-2x.5+2x.3x^2=6x^2+14x-10x^2+6x^3\\
d) 5x-3x^2(4+2x-4x^2)=5x-3x^2.4-3x^2.2x+3x^2.4x^2=5x-12x^2-6x^3+12x^4\\
e) (x-2)(5x^2-4x)=x(5x^2-4x)-2(5x^2-4x)=5x^3-4x^2-10x^2+8x=5x^3-14x^2+8x\\
f) (3x^2+2y)(x-2y)=3x^2(x-2y)+2y(x-2y)=3x^3-6x^2y+2xy-4y^2\\
g) (x^2-2xy+y^2)(x-y)=x^2(x-y)-2xy(x-y)+y^2(x-y)=x^3-x^2y-2x^2y+2xy^2+xy^2-y^3\\
=x^3-3x^2y+3xy^2-y^3\\
h) (2x-1)(3x+1)+(3x+4)(3-2x)\\
=6x^2+2x-3x-1+9x-6x^2+12-8x=11\\
i) (5x+1)(x-2)+(7x-9)(x+4)\\
=5x^2-10x+x-2+7x^2+28x-9x-36\\
=12x^2+10x-38\\
k) (3x-5)(2x+11)-(2x-3)(3x+7)\\
=6x^2+33x-10x-55-(6x^2+14x-9x-21)\\
=6x^2+33x-10x-55-6x^2-14x+9x+21\\
=18x-34\\
2)
a)5x(12x+7)-3x(20x-5)=-100\\
\Leftrightarrow 60x^2+35x-60x^2+15x=-100\\
\Leftrightarrow 50x=-100\\
\Leftrightarrow x=-2\\
b) (2x-1)(3x+1)+(3x-4)(3-2x)=5\\
\Leftrightarrow 6x^2+2x-3x-1+9x-6x^2-12+8x=5\\
\Leftrightarrow 16x-13-5=0\\
\Leftrightarrow 16x=18\\
\Leftrightarrow x=\dfrac{18}{16}=\dfrac{9}{8}\\$
