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

P = 3x² - 2x + 3y² - 2y + 6xy - 100

= (3x² + 6xy + 3y²) - (2x + 2y) - 100

= 3(x² + 2xy + y²) - 2(x + y) - 100

= 3(x + y)² - 2.5 - 100

= 3. 5² -10 - 100

= 75 - 10 - 100 = -35

Q = x³ + y³ - 2x² - 2y² + 3xy(x + y) - 4xy + 3(x+y) +10

= x³ + y³ - 2x² - 2y² + 3x²y + 3xy² - 4xy + 3.5 + 10

= (x³ + 3x²y + 3xy² + y³) - (2x² + 4xy + 2y²) + 15 + 10

= (x + y)³ - 2(x² + 2xy + y²) + 25

= 5³ - 2(x + y)² +25

= 125 - 2. 5² + 25

= 125 - 50 + 25 = 100

\(P=\left(x+2y\right)^2-2\left(x+2y\right)\left(y-1\right)+\left(y-1\right)^2\\ P=\left(x+2y-y+1\right)^2=\left(x+y+1\right)^2\\ Q.sai.đề\\ M=\left(x+y\right)^3-3xy\left(x+y\right)+3xy\\ M=1^3-3xy\left(x+y-1\right)=1-3xy\left(1-1\right)=1-0=1\\ x+y=2\Leftrightarrow\left(x+y\right)^2=4\\ \Leftrightarrow x^2+y^2+2xy=4\\ \Leftrightarrow2xy=4-10=-6\\ \Leftrightarrow xy=-3\\ N=x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)\\ N=2\left(10+3\right)=2\cdot13=26\)