a.

( x-y).(x+y) = ( x-y).x + ( x-y).y = x^2 - x.y + x.y - y^2 = x^2 -y^2

b. 

( x+y)^2=( x+y)( x+y) = ( x+y).x + ( x+y).y = x^2 + x.y + x.y +y^2 = x^2 +2.xy + y^2

c.

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

d/

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

\(a)\)\(\left(x-y\right)\left(x+y\right)\)

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

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

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

\(b)\)\(\left(x+y\right)^2\)

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

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

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

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

Hai công thức này lớp 8 bạn sẽ học ^^

a.(x-y).(x+y)=x.(x+y)-y.(x+y)=x²+xy-(yx+y²)

                                            =x²+xy-yx-y²=x²+0-y²=x²-y²(vì xy=yx mà)

vậy...

b.(x+y)²=(x+y).(x+y)=x.(x+y)+y.(x+y)

                                =x²+xy+yx+y²=x²+2xy+y²

vậy.....

1.

a) (125³x7⁵-175⁵:5):2001²⁰⁰²= 0 : 2001²⁰⁰²= 0

b) 16x64 x8²:(4³x2⁵x16) = 65536 : 576= 1

\(2xy+x-2y=4\\ \Rightarrow x\left(2y+1\right)-2y-1=4-1\\ \Rightarrow x\left(2y+1\right)-\left(2y+1\right)=3\\ \Rightarrow\left(x-1\right)\left(2y+1\right)=3\)

Vì \(x,y\in Z\Rightarrow\left\{{}\begin{matrix}x-1,2y+1\in Z\\x-1,2y+1\inƯ\left(3\right)\end{matrix}\right.\)

Ta có bảng:

Vậy \(\left(x,y\right)\in\left\{\left(0;-2\right);\left(-2;-1\right);\left(2;1\right);\left(4;0\right)\right\}\)

|y|=3

Suy ra: y=3 hoặc y=-3

nếu x=2 và y=3 thì

x^2+2xy^2-3xy-2=2^2+2.2.3^2-3.2.3-2=4+36-18-2=20

Nếu x=2 và y=-3 thì

x^2+2xy^2-3xy-2=2^2+2.2.(-3)^2-3.2.(-3)-2=4+36-(-18)-2=56

B=x²+2xy²-3xy-2

|y|=y=3

Thay x và y vào ta có :

B=2²+2.2.3²-3.2.3-2

B=4+2.2.9-3.2.3-2

B=4+36-18-2

B=20

\(4x-xy+2y=3\)

\(\Rightarrow x\left(4-y\right)-8+2y=3-8\)

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

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

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

\(\Rightarrow\left(x-2\right);\left(y-4\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

Tự xét bảng

\(3y-xy-2x-5=0\)

\(\Rightarrow y\left(3-x\right)-2x=5\)

\(\Rightarrow y\left(3-x\right)+6-2x=5+6\)

\(\Rightarrow y\left(3-x\right)+2\left(3-x\right)=11\)

\(\Rightarrow\left(y+1\right)\left(3-x\right)=11\)

\(\Rightarrow\left(3-x\right);\left(y+1\right)\inƯ\left(11\right)=\left\{\pm1;\pm11\right\}\)

Tự xét

\(2xy-x-y=100\)

\(\Rightarrow x\left(2y-1\right)-y=100\)

\(2x\left(2y-1\right)-\left(2y-1\right)=100+1\)

\(\left(2x-1\right)\left(2y-1\right)=101\)

\(\Rightarrow\left(2x-1\right);\left(2y-1\right)\inƯ\left(101\right)=\left\{\pm1;\pm101\right\}\)

Tự xét bảng

P/s : bài 3 có gì sai ko ?

bài 3 ko sai đâu