\(\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\)

\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\)

\(=\left(x^4-y^4\right)\left(x^4+y^4\right)\)

\(=x^8-y^8\)

\(a,P=x^2-16-x^2+8x-16=8x-32\\ b,=3x^2-6xy+3y^2-2x^2-4xy-2y^2-x^2+y^2\\ =2y^2-10xy=2\cdot9-10\left(-3\right)\cdot2=78\)

\(\frac{y^3-x^3}{x^4-y^4}=\frac{\left(y-x\right)\left(y^2+xy+x^2\right)}{\left(x^2-y^2\right)\left(x^2+y^2\right)}=\frac{-\left(x-y\right)\left(y^2+xy+x^2\right)}{\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)}=\frac{-\left(y^2+xy+x^2\right)}{\left(x+y\right)\left(x^2+y^2\right)}\)

a)

`4*(2y+3x)-3(x-3y)`

`=8y+12x-3x+9y`

`=8y+9y+12x-3x`

`=17y+9x`

b)

`x^2 +2x-x(7x-3)`

`=x^2 +2x-7x^2 +3x`

`=x^2 -7x^2 +2x+6x`

`= -6x^2 +8x`

\(12+3y+4x+xy-12+2y+6x-x-5y\)

\(=9x+xy\)

\(=x\left(y+9\right)\)

12+3y+4x+xy-12+2y+6x-x-5y=

=9x+xy

=x(9+y)

12 + 3y + 4x + xy -12 + 2y + 6x- x - 5y

=9x +xy

=x(y+9)

\(\left(x-y\right)^3+\left(x+y\right)^3\)

\(=x^3-3x^2y+3xy^2-y^3+x^3+3x^2y+3xy^2+y^3\)

\(=2x^3+6xy^2\)

\(\dfrac{x^2-4x+4}{x^3-2x^2-\left(4x-8\right)}=\dfrac{\left(x-2\right)^2}{x^3-2x^2-4x+8}\)

Để biểu thức trên nhận giá trị âm khi \(\dfrac{\left(x-2\right)^2}{x^3-2x^2-4x+8}< 0\)

\(\Rightarrow x^3-2x^2-4x+8< 0\)do \(\left(x-2\right)^2\ge0\)

\(\Leftrightarrow\left(x+2\right)\left(x^2-2x+4\right)-2x\left(x+2\right)< 0\)

\(\Leftrightarrow\left(x+2\right)\left(x-2\right)^2< 0\Leftrightarrow x< -2\)

(-3).8/8.6 rút gọn