cho x-y=7.Tính: \(^{^{x^2\left(x+1\right)-y^2\left(y-1\right)+xy\left(x-y+1\right)-95}}\)
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\(H=x^2\left(x+1\right)-y^2\left(y-1\right)+xy-3xy\left(x-y+1\right)-95\)
\(H=x^3+x^2-y^3+y^2+xy-3x^2y+3xy^2-3xy-95\)
\(\Leftrightarrow H=x^3-3x^2y+3xy^2-y^3+x^2-2xy+y^2-95\)
\(\Leftrightarrow\left(x-y\right)^3+\left(x-y\right)^2-95\)
\(\Leftrightarrow H=7^3+7^2-95=297\)
a) \(x\left(x+2\right)+y\left(y-2\right)-2xy+37\)
\(=x^2+2x+y^2-2y-2xy+37\)
\(=\left(x^2-2xy+y^2\right)+2x-2y+37\)
\(=\left(x-y\right)^2+2\left(x-y\right)+37\)
\(=7^2+2.7+34\)
\(=100\)
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: \(=x^2+2x+y^2-2y-2xy+37\)
\(=\left(x-y\right)^2+2\left(x-y\right)+37\)
\(=7^2+2\cdot7+37=49+14+37=100\)
b: \(=x^3+x^2-y^3+y^2+xy-3xy\cdot\left(7+1\right)-95\)
\(=\left(x^3-y^3\right)+\left(x^2+y^2\right)+xy-24xy-95\)
\(=\left(x-y\right)^3+3xy\left(x-y\right)+\left(x-y\right)^2+2xy-23xy-95\)
\(=7^3+3xy\cdot7+49-21xy-95\)
\(=343+49-95=297\)
\(x^2\left(x+1\right)-y^2\left(y-1\right)+xy\left(x-y+1\right)-95\)
\(=x^3-y^3+x^2+y^2+xy\left(7+1\right)-95\)
\(=\left(x-y\right)^3-3xy\left(x-y\right)+\left(x-y\right)^2+2xy+8xy-95\)
\(=7^3-3.7xy+7^2+2xy+8xy-95\)
\(=-11xy+297\)