Question

solve z(2x - z) (x²+(x-z)²

Answer 1

Step-by-step explanation:

x(y

2

−z

2

)+y(z

2

−x

2

)+z(x

2

−y

2

)=xy

2

−xz

2

+yz

2

−yx

2

+zx

2

−zy

2

Arrange the terms in descending order of power of x.

=−x

2

y+zx

2

+xy

2

−xz

2

−y

z

+yz

2

=−x

2

(y−z)+x(y

2

−z

2

)−yz(y−z)

=−x

2

(y−z)+x(y−z)(y+z)−yz(y−z)

=(y−z)[−x

2

+x(y+z)−yz]

(y−z)[−x

2

+xy+xz−yz]

Arrange the term in bracket in descending order of the power of y.

=(y−z)[xy−yz−x

2

+xz]

=(y−z)[−y(−x+z)+x(−x+z)]

=(x−y)(y−z)(z−x).

Answer 2

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2(x

2

+y

2

+z

2

)−2xy−2yz−2zx=0