A=x^3 + y^3 + 3xy(x+y)
  =x+3x^y+3xy^2+y^3
  =(x+y)^3=2^3=8
B=x^2+2xy+y^2+4
  =(x+y)^2+4=4+4=8

C=x^3+y^3+3xy(x+y)+7(x+y)

  =(x+y)^3+7(x+y)
  =2^3+7.2
  =8+14=22

a) \(A=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)

\(A=x^2+2x+y^2-2y-2xy+37\)

\(A=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)+37\)

\(A=\left(x-y\right)^2+2\left(x-y\right)+37\)

\(A=\left(x-y\right)^2+2\left(x-y\right)+1+36\)

\(A=\left(x-y+1\right)^2+36\)

Thay x - y = 7 vào A

\(A=\left(7+1\right)^2+36\)

\(A=8^2+36\)

\(A=64+36\)

\(A=100\)

b) \(B=x^3+x^2-y^3+y^2+xy-3x^2y+3xy^2-3xy-9\)

\(B=\left(x^3-3x^2y+3xy^2-y^3\right)+\left(x^2+xy-3xy+y^2\right)-9\)

\(B=\left(x-y\right)^3+\left(x^2-2xy+y^2\right)-9\)

\(B=\left(x-y\right)^3+\left(x-y\right)^2-9\)

Thay x - y = 7 vào B

\(B=7^3+7^2-9\)

\(B=343+49-9\)

\(B=383\)

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

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

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

Thay x - y = 7 vào C

\(C=7^3-7^2\)

\(C=343-49\)

\(C=294\)

d) \(D=x^2\left(x+1\right)-y^2\left(y-1\right)+xy-3xy\left(x-y+1\right)-95\)

\(D=x^3+x^2-y^3+y^2+xy-3x^2y+3xy^2-3xy-95\)

\(D=\left(x^3-3x^2y+3xy^2-y^3\right)+\left(x^2-2xy+y^2\right)-95\)

\(D=\left(x-y\right)^3+\left(x-y\right)^2-95\)

Thay x - y = 7 vào D

\(D=7^3+7^2-95\)

\(D=343+49-95\)

\(D=297\)

Câu a) sai đề em ơi

Đề đúng là: x² + y² = (x + y)² - 2xy

Giải theo đúng đề nè:

a) x² + y²

= x² + y² + 2xy - 2xy

= (x + y)² - 2xy

b) Đề cũng sai. Đề đúng phải là: x³ + y³ = (x + y)³ - 3xy(x + y)

Giải đề đúng là:

x³ + y³ = x³ + y³ + 3x²y + 3xy² - 3x²y - 3xy²

= (x + y)³ - 3xy(x + y)

c) x³ - y³ = x³ - 3x²y + 3xy² - y³ + 3x²y - 3xy²

= (x - y)³ + 3xy(x - y)

giải :

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

= \(x^3-3x^2y+3xy^2-y^3-x^2+2xy-y^2\)

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

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

a ) có \(x^2+y^2+4x-2xy+4y+2019=\left(x-y\right)^2+4\left(x-y\right)+2019=49+28+2019=2096\)

b) \(x^3-3xy\left(x-y\right)-y^3-x^2+2xy-y^2=\left(x-y\right)^3-\left(x-y\right)^2=343-49=294\)

c)\(x^2\left(x+1\right)-y^2\left(y-1\right)+xy-3xy\left(x-y+1\right)=x^3-y^3+x^2+y^2+xy-3x^2y+3xy^2-3xy=\left(x-y\right)^3+\left(x-y\right)^2=343+49=392\)