Đặt \(x^2+y^2=a\)

Khi đó ta được: \(P=\left(a+2\right)^3-\left(a-2\right)^3-12a^2\)

\(\Leftrightarrow P=a^3.6a^2+12a+8-a^3+6a^2-12a+8-12a^2\)

\(\Leftrightarrow P=\left(a^3-a^3\right)+\left(6a^2+6a^2-12a^2\right)+\left(12a-12a\right)+8+8\)

\(\Leftrightarrow P=16\)

Vậy \(P=16\) tại \(x=2019\) và \(y=2020\)

1: \(C=\left(x-\dfrac{4xy}{x+y}+y\right):\left(\dfrac{x}{x+y}+\dfrac{y}{y-x}+\dfrac{2xy}{x^2-y^2}\right)\)

\(=\dfrac{\left(x+y\right)^2-4xy}{x+y}:\left(\dfrac{x}{x+y}-\dfrac{y}{x-y}+\dfrac{2xy}{\left(x-y\right)\left(x+y\right)}\right)\)

\(=\dfrac{x^2+2xy+y^2-4xy}{x+y}:\dfrac{x\left(x-y\right)-y\left(x+y\right)+2xy}{\left(x+y\right)\left(x-y\right)}\)

\(=\dfrac{x^2-2xy+y^2}{x+y}:\dfrac{x^2-xy-xy-y^2+2xy}{\left(x+y\right)\left(x-y\right)}\)

\(=\dfrac{\left(x-y\right)^2}{x+y}\cdot\dfrac{x^2-y^2}{x^2-y^2}=\dfrac{\left(x-y\right)^2}{x+y}\)

2: \(\left(x^2-y^2\right)\cdot C=-8\)

=>\(\left(x-y\right)\left(x+y\right)\cdot\dfrac{\left(x-y\right)^2}{x+y}=-8\)

=>\(\left(x-y\right)^3=-8\)

=>x-y=-2

=>x=y-2

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

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

\(=\left(y-1\right)\left[\left(y-2\right)^2-y^2\right]+3xy+xy\)

\(=\left(y-1\right)\left(-4y+4\right)+4xy\)

\(=-4\left(y-1\right)^2+4y\left(y-2\right)\)

\(=-4y^2+8y-4+4y^2-8y\)
=-4

b, \(C=x^2-5x+5y-2xy+y^2+6\)

\(=x^2-2xy+y^2-5\left(x-y\right)+6\)

\(=\left(x-y\right)^2-5\left(x-y\right)+6\)

\(=49-35+6=20\) ( do x - y = 7 )

Vậy C = 20

A= (\(\dfrac{1}{2}\)+\(\dfrac{3}{4}\)-\(\dfrac{4}{4}\))X²Y² = \(\dfrac{1}{4}\)x²y²

rất tiếc em mới học lớp 6

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