a: \(x-y=10\)
=>\(\left(x-y\right)^2=10^2=100\)
=>\(x^2+y^2-2xy=100\)
=>\(5-2xy=100\)
=>2xy=-95
=>\(xy=-\dfrac{95}{2}\)
\(M=x\left(x^2+y^2\right)-y\left(x^2+y^2\right)+3\)
\(=\left(x^2+y^2\right)\left(x-y\right)+3\)
\(=10\cdot5+3=50+3=53\)
b: \(P=4x^4+7x^2y^2+3y^4+5y^2\)
\(=4x^4+4x^2y^2+3x^2y^2+3y^4+5y^2\)
\(=4x^2\left(x^2+y^2\right)+3y^2\left(x^2+y^2\right)+5y^2\)
\(=4x^2\cdot5+3y^2\cdot5+5y^2\)
\(=20x^2+20y^2=20\left(x^2+y^2\right)=20\cdot5=100\)
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