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

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

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

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

\(=7^2+2.7+34\)

\(=100\)

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

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

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

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

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

\(=297\)

A=2y^3-4y^2-28y+294

a: \(=x^2+2x+y^2-2y-2xy+37\)

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

\(=7^2+2\cdot7+37=49+14+37=100\)

b: \(=x^3+x^2-y^3+y^2+xy-3xy\cdot\left(7+1\right)-95\)

\(=\left(x^3-y^3\right)+\left(x^2+y^2\right)+xy-24xy-95\)

\(=\left(x-y\right)^3+3xy\left(x-y\right)+\left(x-y\right)^2+2xy-23xy-95\)

\(=7^3+3xy\cdot7+49-21xy-95\)

\(=343+49-95=297\)

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

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

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

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

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

\(A=x^3-y^3-21xy\)

\(A=\left(x-y\right).\left(x^2+xy+y^2\right)-21xy\)

\(A=7.\left(x^2+xy+y^2\right)-21xy\)

\(A=7.\left(x^2+xy+y^2+3xy\right)\)

\(A=7.\left(x^2+2xy+y^2+2xy\right)\)

\(A=7.\text{[}\left(x+y\right)^2+2xy\text{]}\)

\(A=7.\left(7^2+2xy\right)\)

\(A=7^3+14xy\)

Ngáo rồi @@

\(\)

\(A=x^3-y^3-21xy\)

\(\Rightarrow A=\left(x-y\right)\left(x^2+xy+y^2\right)-21xy\)

\(\Rightarrow A=7\left(x^2+xy+y^2\right)-21xy\)

\(\Rightarrow A=7\left(x^2+xy+y^2-3xy\right)\)

\(\Rightarrow A=7\left(x^2+y^2-2xy\right)\)

\(\Rightarrow A=7\left(x-y\right)^2\)

\(\Rightarrow A=7.7^2\)

\(\Rightarrow A=7.49\)

\(\Rightarrow A=343\)

ak trách j :V lộn dấu :V 

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

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

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

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

\(=297\)

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