Question

Phân tích:

a)(x-y)³+(y-z)³+(z-x)³

b)x.(y²-z²)+y.(z²-x²)+z.(x²-y²)

c)xy.(x-y)-xz.(x+z)-yz.(zx-y+z)

d)x.(y+z)²+y.(z-x)²+z.(x+y)²-4xyz

Answer 1

a ) \(\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3\)

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

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

Answer 2

b)\(x\left(y^2-z^2\right)+z\left(x^2-y^2\right)+y\left(z^2-x^2\right)\)

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

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

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

=\(\left(y-z\right)\left(z-x\right)\left(-\left(y+z\right)+z+x\right)\)

=\(\left(y-z\right)\left(z-x\right)\left(x-y\right)\)