\(1)A=2x\left(x-y\right)-y\left(y-2x\right)\)

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

\(=2x^2-y^2=2.\left(-\dfrac{2}{3}\right)^2-\left(-\dfrac{1}{3}\right)^2\)

\(=\dfrac{8}{9}-\dfrac{1}{9}=\dfrac{7}{9}\)

\(2)B=5x\left(x-4y\right)-4y\left(y-5x\right)\)

\(=5x^2-20xy-4y^2+20xy\)

\(=5x^2-4y^2=5.\left(-\dfrac{1}{5}\right)^2-4.\left(-\dfrac{1}{2}\right)^2=\dfrac{1}{5}-1=-\dfrac{4}{5}\)

\(3)C=\text{x.(x^2-y^2)-x^2(x+y)+y(x^2-x)}\)

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

\(=-xy\left(x+1\right)\)

\(=\dfrac{1}{2}.100\left(100+1\right)=50.101=5050\)

\(a. 2x(3x^2-5x+3) = 6x^3-10x^2+6x \)

\(b. -2x(x^2+5x-3) = -2x^3-10x^2+6x\)

c. \(-\dfrac{1}{2}x^2\left(2x^3-4x+3\right) =-x^5+2x^3-\dfrac{3}{2}x^2\)
\(d.\left(2x-1\right)\left(x^2+5-4\right)=\left(2x-1\right)\left(x^2+1\right)=2x^3+2x-x^2-1\)
e. \(-\left(5x-4\right)\left(2x+3\right)=10x^2+15x-8x-12=-10x^2+7x-12\)

f.\(\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)

g.\(\left(3x-4\right)\left(x+4\right)+\left(5-x\right)\left(2x^2+3x-1\right)=3x^2+12x-4x-16+10x^2+15x-5-2x^3-3x^2+x=-2x^3+10x^2+24x-21\)

e. \(7x\left(x-4\right)-\left(7x+3\right)\left(2x^2-x+4\right)=7x^2-28x-14x^3+7x^2-28x-6x^2+3x+-12=-14x^3+8x^2-53x-12\)

\(\frac{x+1}{x-2}+\frac{x-1}{x+2}=\frac{2\left(x^2+2\right)}{x^2-4}\left(x\ne\pm2\right)\)

\(\Leftrightarrow\frac{\left(x+1\right)\left(x+2\right)+\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}=\frac{2\left(x^2+2\right)}{x^2-4}\)

\(\Leftrightarrow\frac{2x^2+4}{x^2-4}=\frac{2x^2+4}{x^2-4}\)

Vậy phương trình này có vô số nghiệm x thỏa mãn trừ x khác 2 và -2

Bài 4:

a: \(=7xy\left(2-3-4\right)=-35xy\)

b: \(=\left(x-5\right)\left(x+y\right)\)

c: \(=10x\left(x-y\right)+8\left(x-y\right)=2\left(x-y\right)\left(5x+4\right)\)

d: \(=\left(x+y\right)^3-\left(x+y\right)\)

=(x+y)(x+y+1)(x+y-1)

e: =x^2+8x-x-8

=(x+8)(x-1)

f: \(=2x^2-4x+x-2=\left(x-2\right)\left(2x+1\right)\)

g: =-5x^2+15x+x-3

=(x-3)(-5x+1)

h: =x^2-3xy+xy-3y^2

=x(x-3y)+y(x-3y)

=(x-3y)*(x+y)

Bài 4:

a: \(=7xy\left(2-3-4\right)=-35xy\)

b: \(=\left(x-5\right)\left(x+y\right)\)

c: \(=10x\left(x-y\right)+8\left(x-y\right)=2\left(x-y\right)\left(5x+4\right)\)

d: \(=\left(x+y\right)^3-\left(x+y\right)\)

=(x+y)(x+y+1)(x+y-1)

e: =x^2+8x-x-8

=(x+8)(x-1)

f: \(=2x^2-4x+x-2=\left(x-2\right)\left(2x+1\right)\)

g: =-5x^2+15x+x-3

=(x-3)(-5x+1)

h: =x^2-3xy+xy-3y^2

=x(x-3y)+y(x-3y)

=(x-3y)*(x+y)

Bài 3:

a: =>3x^2-6x-x-3x^2=14

=>-7x=14

=>x=-2

b: \(\Leftrightarrow2x^2+10x-x-5-2x^2-9x-x-4.5=3.5\)

=>-x-9,5=3,5

=>-x=12

=>x=-12

c: =>\(3x-3x^2+9x=36\)

=>-3x^2+12x-36=0

=>x^2-6x+12=0(loại)

d: \(\Leftrightarrow3x^2-3x+x-1+4x-3x^2=5\)

=>2x=6

=>x=3