Question

CM:

a,-(x+y)^2-(x-y)^2=4xy

b,-3(x^2+y^2+z^2)-(x-y)^2-(y-x)^2-(z-x)=(x+y+z)^2

Answer 1

a) \(\left(x+y\right)^2-\left(x-y\right)^2=\left(x^2+2xy+y^2\right)-\left(x^2-2xy+y^2\right)=2xy+2xy=4xy\)

Answer 2

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

\(=-x^2-2xy-y^2-x^2+2xy-y^2=4xy=VP\)

Answer 3

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

\(=3x^2+3y^2+3z^2-x^2+2xy-y^2-y^2+2yz-z^2-z^2+2zx-x^2\)

\(=x^2+y^2+z^2+2xy+2yz+2zx=\left(x+y+z\right)^2=VP\)

Answer 4

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