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

Bài 2:

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

\(N=x^2+y^2=\left(x-y\right)^2+2xy=9+2.10=29\)

\(P=x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3=\left(-3\right)^3=-27\)

\(Q=x^3-y^3=\left(x-y\right)^3+3xy\left(x-y\right)=\left(-3\right)^3+3.10.\left(-3\right)=-117\)

Bài 1:

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

b)  \(B=x^2+y^2=\left(x+y\right)^2-2xy=\left(-1\right)^2-2.\left(-12\right)=25\)

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

d)  \(D=x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)=\left(-1\right)^3-3.\left(-12\right).\left(-1\right)=-37\)

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

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

\(D=343+49-95\)

\(D=297\)

Ta có: x^3 -3xy(x-y) -y^3 -x^2 + 2xy-y^2

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

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

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

=11( x^2 -2xy+y^2 -x+y)

= 11[ (x-y)^2 -(x-y)]

= 11[ 11^2 -11]

= 11^3 -11^2=...

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

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

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

\(=7\)

\(a,=2x^2-\dfrac{3}{2}y+3x\)

\(b,\)bt để chia hết cho x+2 là:\(2x^3+x^2-x+10\)

\(\Rightarrow m=12\)

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:

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

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

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

Thay \(x-y\) vào, được:

\(M=7^3-7^2=294\)

Vậy ...

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

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

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

\(\Leftrightarrow N=\left[x^3-y^3-3xy\left(x-y\right)\right]+\left(x^2-2xy+y^2\right)-95\)

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

Thay \(x-y\) vào, được:

\(N=7^3+7^2-95=297\)

Vậy ...

Chúc bạn học tốt!