a) \(\left(xy+1\right)^2-\left(x+y\right)^2\)

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

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

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

\(=\left(x+y-x+y\right)\left[\left(x^2+2xy+y^2\right)+x^2-y^2+\left(x^2-2xy+y^2\right)\right]\)

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

\(=2y\left(3x^2+y^2\right)\)

c) \(3x^4y^2+3x^3y^2+3xy^2+3y^2\)

\(=3y^2\left(x^4+x^3+x+1\right)\)

d) \(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)\)

\(=4\left[\left(x^2-y^2\right)-2\left(x-ay\right)-\left(a^2-1\right)\right]\)

\(=4\left[\left(x^2-y^2\right)-\left(2x-2ay\right)-\left(a^2-1\right)\right]\)

\(=4\left(x^2-y^2-2x+2ay-a^2+1\right)\)

P/s: Ko chắc!

c/

\(=3y^2\left(x^4+x^3+x+1\right)\)

\(=3y^2\left[x^3\left(x+1\right)+x+1\right]\)

\(=3y^2\left(x^3+1\right)\left(x+1\right)\)

\(=3y^2\left(x+1\right)^2\left(x^2-x+1\right)\)

d/

\(=\left(4x^2-8x+4\right)-\left(4y^2-8ay+4a^2\right)\)

\(=4\left(x-1\right)^2-4\left(y-a\right)^2\)

\(=4\left[\left(x-1\right)^2-\left(y-a\right)^2\right]\)

\(=4\left(x-1-y+a\right)\left(x-1+y-a\right)\)

a) Ta có: \(4\left(2-x\right)^2+xy-2y\)

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

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

\(=\left(x-2\right)\left(4x-8+y\right)\)

b) Ta có: \(3a^2x-3a^2y+abx-aby\)

\(=3a^2\left(x-y\right)+ab\left(x-y\right)\)

\(=\left(x-y\right)\left(3a^2+ab\right)\)

\(=a\left(x-y\right)\left(3a+b\right)\)

c) Ta có: \(x\left(x-y\right)^3-y\left(y-x\right)^2-y^2\left(x-y\right)\)

\(=x\left(x-y\right)^3-y\left(x-y\right)^2-y^2\left(x-y\right)\)

\(=\left(x-y\right)\left[x\left(x-y\right)^2-y\left(x-y\right)-y^2\right]\)

\(=\left(x-y\right)\left[x\left(x^2-2xy+y^2\right)-yx+y^2-y^2\right]\)

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

d) Ta có: \(2ax^3+6ax^2+6ax+18a\)

\(=2ax^2\left(x+3\right)+6a\left(x+3\right)\)

\(=\left(x+3\right)\left(2ax^3+6a\right)\)

\(=2a\left(x+3\right)\left(x^3+3\right)\)

e) Ta có: \(x^2y-xy^2-3x+3y\)

\(=xy\left(x-y\right)-3\left(x-y\right)\)

\(=\left(x-y\right)\left(xy-3\right)\)

a) Ta có: \(\left(3-xy^2\right)^2-\left(2+xy^2\right)^2\)

\(=\left[\left(3-xy^2\right)-\left(2+xy^2\right)\right]\cdot\left[\left(3-xy^2\right)+\left(2+xy^2\right)\right]\)

\(=\left(3-xy^2-2-xy^2\right)\cdot\left(3-xy^2+2+xy^2\right)\)

\(=5\cdot\left(1-2xy^2\right)\)

\(=5-10xy^2\)

b) Ta có: \(9x^2-\left(3x-4\right)^2\)

\(=\left[3x-\left(3x-4\right)\right]\left[3x+\left(3x-4\right)\right]\)

\(=\left(3x-3x+4\right)\cdot\left(3x+3x-4\right)\)

\(=4\cdot\left(6x-4\right)\)

\(=24x-16\)

c) Ta có: \(\left(a-b^2\right)\left(a+b^2\right)\)

\(=a^2-b^4\)

d) Ta có: \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)\)

\(=\left(a^2+2a\right)^2-9\)

\(=a^4+4a^3+4a^2-9\)

e) Ta có: \(\left(x-y+6\right)\left(x+y-6\right)\)

\(=x^2+xy-6x-yx-y^2+6y+6x+6y-36\)

\(=x^2-y^2+12y-36\)

f) Ta có: \(\left(y+2z-3\right)\left(y-2z-3\right)\)

\(=\left(y-3\right)^2-\left(2z\right)^2\)

\(=y^2-6y+9-4z^2\)

g) Ta có: \(\left(2y-5\right)\left(4y^2+10y+25\right)\)

\(=\left(2y\right)^3-5^3\)

\(=8y^3-125\)

h) Ta có: \(\left(3y+4\right)\left(9y^2-12y+16\right)\)

\(=\left(3y\right)^3+4^3\)

\(=27y^3+64\)

i) Ta có: \(\left(x-3\right)^3+\left(2-x\right)^3\)

\(=\left(x-3\right)^3-\left(x-2\right)^3\)

\(=x^3-9x^2+27x-27-\left(x^3-6x^2+12x-8\right)\)

\(=x^3-9x^2+27x-27-x^3+6x^2-12x+8\)

\(=-3x^2+15x-19\)

j) Ta có: \(\left(x+y\right)^3-\left(x-y\right)^3\)

\(=\left[\left(x+y\right)-\left(x-y\right)\right]\cdot\left[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\right]\)

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

\(=2y\cdot\left(3x^2+y^2\right)\)

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

\(2xy+2x-y=8\)

\(\Rightarrow2x\left(y+1\right)-\left(y+1\right)=8-1\)

\(\Rightarrow\left(y+1\right)\left(2x-1\right)=7\)

\(\Rightarrow\left(2x-1\right)\left(y+1\right)\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

\(TH1:\hept{\begin{cases}2x-1=1\\y+1=7\end{cases}\Rightarrow\hept{\begin{cases}x=1\\y=6\end{cases}}}\)  \(TH2:\hept{\begin{cases}2x-1=-1\\y+1=-7\end{cases}\Rightarrow\hept{\begin{cases}x=0\\y=-8\end{cases}}}\)

\(TH3:\hept{\begin{cases}2x-1=7\\y+1=1\end{cases}\Rightarrow\hept{\begin{cases}x=4\\y=0\end{cases}}}\)         \(TH4:\hept{\begin{cases}2x-1=-7\\y+1=-1\end{cases}\Rightarrow\hept{\begin{cases}x=-4\\=0\end{cases}}}\)      

Vậy \(\left(x;y\right)\in\left\{\left(1;6\right);\left(0,-8\right);\left(4;0\right);\left(-4;0\right)\right\}\)

đề bài là j vậy

Áp dụng tính chất dãy tỉ số bằng nhau

\(\frac{x}{5}=\frac{y}{7}=\frac{z}{9}=\frac{x-y+z}{5-7+9}=\frac{315}{7}=45\)

  suy ra:   x/5 = 45   =>  x  =  225

               y/7 = 45  =>  y  =  315

               z/9 = 45  =>  z  =  405

Bài 1: 

b) \(\left(2x^2-3y\right)^3\)

\(=8x^6-3\cdot4x^4\cdot3y+3\cdot2x^2\cdot9y^2-27y^3\)

\(=8x^6-36x^4y+54x^2y^2-27y^3\)

Bạn nên đánh lại đề bài a nhé.

b: 

=>x(y-3)+3(y-3)=17

=>(y-3)(x+3)=17

\(\Leftrightarrow\left(x+3,y-3\right)\in\left\{\left(1;17\right);\left(17;1\right);\left(-1;-17\right);\left(-17;-1\right)\right\}\)

hay \(\left(x,y\right)\in\left\{\left(-2;20\right);\left(14;4\right);\left(-4;-14\right);\left(-20;2\right)\right\}\)

a: =>x(2y+3)+2(2y+3)=5

=>(2y+3)(x+2)=5

\(\Leftrightarrow\left(2y+3;x+2\right)\in\left\{\left(1;5\right);\left(-1;-5\right);\left(5;1\right);\left(-5;-1\right)\right\}\)

hay \(\left(y,x\right)\in\left\{\left(-1;3\right);\left(-2;-7\right);\left(1;-1\right);\left(-4;-3\right)\right\}\)